00
CO
Columbia
teachers College
Educational IReprints
' Wo. 3
MEMORY
A CONTRIBUTION TO EXPERIMENTAL
PSYCHOLOGY
BY
HERMANN EBBINGHAUS
PRIVAT DOCENT IN PHILOSOPHY AT THE UNIVERSITY OF BERLIN
(1885)
De subjecto vetustissimo
novissimam promovemus scienttam"
TRANSLATED BY
HENRY A. RUGER, Pn.D.
ASSISTANT PROFESSOR OF EDUCATIONAL PSYCHOLOGY, TEACHERS
COLLEGE, COLUMBIA UNIVERSITY
AND
CLARA E. BUSSENIUS
PUBLISHED BY
flfolkgr, Ctttmbte Ihmir rmti;
NEW YORK CITY
1913
Lb
i 06,3
602497
TRANSLATORS' INTRODUCTION
The publication by Ebbinghaus of the results of his experi-
mental investigation of memory (1885) marks the application of
precise scientific method to the study of the " higher mental pro-
cesses." By his invention of nonsense syllables as the material to
be thus employed Ebbinghaus signalised the growing independ-
ence of experimental psychology from physics and physiology.
For educational psychology his work is of especial importance
because the field in which he worked was that of the ideational
processes and because the problems which he attacked were
functional and dynamic. The problem of the most efficient dis-
tribution of repetitions in committing material to memory may
be taken to illustrate the identity in the nature of the questions
investigated by him and those of especial interest to us to-day.
Despite the fact that his experiments were performed only on
himself and that the numerical results obtained are consequently
limited in significance, his work stands as an embodiment of
the essentials of scientific method. On account of its historical
importance and also because of its intrinsic relation to present
day problems and methods Ebbinghaus's investigation should
be known as directly as possible by all serious students of psy-
chology. To facilitate this acquaintance is the purpose of this
translation.
The translators wish to acknowledge their indebtedness to
Professors Edward L. Thorndike, Robert S. Woodworth, and
E. W. Bagster-Collins of Columbia University, to Professor
Walter Dill Scott of Northwestern University and to Mrs. H. A.
Ruger for assistance in revising manuscript and proof.
in
AUTHOR'S PREFACE
In the realm of mental phenomena, experiment and measure- i
ment have hitherto been chiefly limited in application to sense
perception and to the time relations of mental processes. By
means of the following investigations we have tried to go a step
farther into the workings of the mind and to submit to an
experimental and quantitative treatment the manifestations of
memory. The term, memory, is to be taken here in its broadest
sense, including Learning, Retention, Association and Repro-
duction.
The principal objections which, as a matter of course, rise
against the possibility of such a treatment are discussed in
detail in the text and in part have been made objects of investi-
gation. I may therefore ask those who are not already convinced
a priori of the impossibility of such an attempt to postpone
their decision about its practicability.
The author will be pardoned the publication of preliminary
results in view of the difficulty of the subject investigated and
the time-consuming character of the tests. Justice demands
that the many defects due to incompleteness shall not be raised
as objections against such results. The tests were all made upon
myself and have primarily only individual significance. Naturally
they will not reflect exclusively mere idiosyncrasies of my mental
organisation; if the absolute values found are throughout only
individual, yet many a relation of general validity will be found
in the relation of these numbers to each other or in the relations
of the relations. But where this is the case and where it is
not, I can hope to decide only after finishing the further and
comparative experiments with which I am occupied.
TABLE OF CONTENTS
Chapter Page
Preface . . . v
I. OUR KNOWLEDGE CONCERNING MEMORY .... i
Section i. Memory in its Effects i
2. Memory in its Dependence .... 3
3. Deficiencies in our Knowledge concerning
Memory ....... 4
II. THE POSSIBILITY OF ENLARGING OUR KNOWLEDGE OF MEMORY 7
Section 4. The Method of Natural Science ... 7
5. The Introduction of Numerical Measurements
for Memory Contents ..... 8
6. The Possibility of Maintaining the Constancy
of Conditions Requisite for Research . . it
7. Constant Averages . . . . . 12
8. The Law of Errors 15
9. Resume . . . . . . . . 19
" 10. The Probable Error 30
III. THE METHOD OF INVESTIGATION . . . . . . 22
Section n. Series of Nonsense Syllables 23
12. Advantages of the Material . . . . 23
13. Establishment of the Most Constant Experi-
mental Conditions Possible . . . . 24
14. Sources of Error 26
15. Measurement of Work Required ... 30
" 16. Periods of the Tests 33
IV. THE UTILITY OF THE AVERAGES OBTAINED . . . . 34
Section 17. Grouping of the Results of the Tests . . 34
" 18. Grouping of the Results of the Separate Series 41
V. RAPIDITY OF LEARNING SERIES OF SYLLABLES AS A FUNCTION \/
OF THEIR LENGTH ....... 46
Section 19. Tests Belonging to the Later Period . . 46
20. Tests Belonging to the Earlier Period . . 49
21. Increase in Rapidity of Learning in the Case
of Meaningful Material .... 50
VI. RETENTION AS A FUNCTION OF THE NUMBER OF REPETITIONS 52 ^
Section 22. Statement of the Problem . . . . 52
23. The Tests and their Results .... 54
24. The Influence of Recollection . . . 58
25. The Effect of a Decided Increase in the
Number of Repetitions .... 59
vii
viii Table of Contents
Chapter Page
VII. RETENTION AND OBLIVISCENCE AS A FUNCTION OF THE TIME 62
Section 26. Explanations of Retention and Obliviscence . 62
" 27. Methods of Investigation of Actual Conditions 65
28. Results 67
" 29. Discussion of Results ..... 76
" 30. Control Tests 79
VIII. RETENTION AS A FUNCTION OF REPEATED LEARNING . . 81
Section 31. Statement of the Problem and the Investigation 81
" 32. Influence of the Length of the Series . . 84
" 33. Influence of Repeated Learning ... 85
" 34. Influence of the Separate Repetitions . . 87
IRRETENTION AS A FUNCTION OF THE ORDER OF SUCCESSION OF
THE MEMBERS OF THE SERIES ..... 90
Section 35. Association according to Temporal Sequence
and its Explanation ..... 90
36. Methods of Investigation of Actual Behavior 95
37. Results. Associations of Indirect Sequence . 99
38. Experiments with Exclusion of Knowledge . 101
39. Discussion of Results ..... 106
40. Reverse Associations . . . . .no
41. The Dependence of Associations of Indirect
Sequence upon the Number of Repetitions . 114
42. Indirect Strengthening of Associations . . 117
MEMORY
CHAPTER I
Section i. Memory in its Effects
The language of life as well as of science in attributing a
memory to the mind attempts to point out the facts and their
interpretation somewhat as follows:
Mental states of every kind,— sensations, feelings, . ideas, — {
which were at one time present Jn consciousness and then have .
disappeared from it. have not with their disappearance absolutely
ceased to exist. Although the inwardly-turned look may no
longer be able to find them, nevertheless they have not been
utterly destroyed and annulled, but in a certain manner they,
continue to exfet, sjoreiTul^jro to speak, .in. the memory. We
cannot^of course, directly observe_their present existence, but
it is revealed by the effects which come to our knowledge with
a certainty like that with which we infer the existence of the
stars below the horizon. These effects are of different kinds.
In a first group of cases we can call back into conscious-
ness by an exertion of the will directed to this purpose the
seemingly lost states (or, indeed, in case these consisted in imme-
diate sense-perceptions, we can recall their true memory images) :
that is, we can reproduce them voluntarily. During attempts of
this sort, — that is, attempts to recollect— all sorts of images
toward which our aim was not directed, accompany the desired
images to the light of consciousness. Often, indeed, the latter
entirely miss the goal, but as a general thing among the repre- ^
sentations is found the one which we sought, and it is imme- \
diately recognised as something formerly experienced. It would
be absurd to suppose that our will has created it anew and, as
it were, out of nothing; it must have been present somehow
i
2 Memory
or somewhere. The will, so to speak, has only discovered
it and brought it to us again.
In a second group of cases this survival is even more striking.
Often, even after years, mental states once present in conscious-
ness return to it with apparent spontaneity and without any act
of the will; that is, they are reproduced^ involuntarily. Here,
also, in the majority of cases we at once recognise the returned
mental state as one that has already been experienced; that is,
we remember it. Under certain conditions, however, this ac-
companying consciousness is lacking, and we know only indi-
rectly that the " now " must be identical with the " then " ; yet
we receive in this way a no less valid proof for its existence
during the intervening time. As more exact observation teaches
us, the occurrence of these involuntary reproductions is not an
entirely random and accidental one. On the contrary they are
j^ brought about through the instrumentality of other, immediately
present mental images. Moreover they occur in certain regular
ways which in general terrns are described under the so-called
ffrAlaws of association^—
Finally there is a third and large group to be reckoned with
here. The vanished mental states give indubitable proof of their
continuing existence .even if they themselves do not return to
V consciousness at all, or at least not exactly at the given time.
Employment of a certain range of thought facilitates under cer-,
tain conditions the employment of a similar range of thought,
even if the former does not come before the mind directly either
in its methods or in its results. The boundless domain of the
\ effect of accumulated experiences belongs here. This effect
results from the frequent conscious occurrence of any condi-
tion or process, and consists in facilitating the occurrence and
progress of similar processes. This effect is not fettered by
the condition that the factors constituting the experience shall
return in toto to consciousness. This may incidentally be the
case with a part of them; it must not happen to a too great
extent and with too great clearness, otherwise the course of the
present process will immediately be disturbed. Most of these
experiences remain concealed from consciousness and yet pro-
duce an effect which is significant and which authenticates their
previous existence.
Our Knowledge Concerning Memory 3
Section 2. Memory in its Dependence
Along' with this bare knowledge of the existence of memory
and its effects, there is abundant knowledge concerning the
conditions upon which depend the vitality of that inner survnljal'
as well as the fidelity and promptness of the reproduction. \\
How differently do different individuals behave in this
respect! One retains and reproduces well; another, poorly.
And not only does this comparison hold good when different
individuals are compared with each other, but also when different
phases of the existence of the same individual are compared:
morning and evening, youth and old age, find him different in/
this respect.
Differences in the content of the thing to be reproduced are \
of great influence. Melodies may become a source of torment _'_
by the undesired persistency of their return. Forms and colors
are not so importunate; and if they do return, it is with notice-
able loss of clearness and certainty. The musician writes for the
orchestra what his inner voice sings to him; the painter rarely
relies without disadvantage solely upon the images which his
inner eye presents to him; nature gives him his forms, study1
governs his combinations of them. It is with something of a
struggle that past states of feeling are realized; when realized,
and this is often only through the instrumentality of the move-
ments which accompanied them, they are but pale shadows of
themselves. Emotionally true singing is rarer than technically
correct singing.
If the two foregoing points of view are taken together —
differences in individuals and Differences in content — an endless
number of differences come to light. One individual overflows
with poetical reminiscences, another directs symphonies from
memory, while numbers and formulae, which come to a third
without effort, slip away from the other two as from a polished
stone.
Veryjyreat is the^dependence _ of retention and-jffimvlnciion
upon the inten^iyoijhe_attention and interest which were
attached to the mental states the first time they were present.
The burnt child shuns the fire, and the dog which has
been beaten runs from the whip,y after a single vivid experi-
ence. People in whom we are" interested we may see daily
4 Memory
and yet not be able to recall the color of their hair or of their
eyes.
Under ordinary circumstances, indeed, frequent repetitions are
indispensable in order to make possible the reproduction of a
given content. Vocabularies, discourses, and poems of any length
cannot be learned by a single repetition even with the greatest
concentration of attention on the part of an individual of very
great ability. By a sufficient number of repetitions their final
mastery is ensured, and by additional later reproductions gain
in assurance and ease is secured.
") / Left to itself every mental content gradually loses its capacity
/ for being revived, or at least suffers^ loss_in this regard under
\ the influence of time. Facts crammed at examination time soon
vanish, if they were not sufficiently grounded by other study
and later subjected to a sufficient review. But even a thing so
early and deeply founded as one's mother tongue is noticeably
impaired if not used for several years.
Section 3. Deficiencies in our Knowledge concerning Memory
The foregoing sketch of our knowledge concerning memory
makes no claim to completeness. To it might be added such a
series of propositions known to psychology as the following:
'' He who learns quickly also forgets quickly," " Relatively long
series of ideas are retained better than relatively short ones,"
Old people forget most quickly the things they learned last,"
and the like. Psychology is wont to make the pictu-re rich with
anecdote and illustration. But — and this is the main point —
even if we particularise our knowledge by a most extended use
(.of illustrative material, everything that we can say retains the
indefinite, general, and comparative character of the propositions
quoted above. Our information comes almost exclusively from
the observation of extreme and especially striking cases. We
are able to describe these quite correctly in a general way and
in vague expressions of more or less. We suppose, again quite
correctly, that the same influences exert themselves, although
in a less degree, in the case of the inconspicuous, but a thousand-
fold more frequent, daily activities of memory. But if our
i .' curiosjty__ carries us further and we crave more specific and
detailed information concerning these dependencies and inter-
Our Knowledge Concerning Memory 5
dependencies, both those already mentioned and others, — if we
put questions, so to speak, concerning their inner structure — our
answer is silence. HQW does the disappearance of the ability
to reproduce, forgetfulness, depend upon the length of ,
time ^during which ^a_mp_e±kiQps have taken place? What,
proportion does the increase in the certainty of reproduction!
bear to the number ojj^petitions ? How do these relations vary
with the greater or less intensity of the interest in the thing to'
be reproduced ? These and similar questions no one can answer.
This inability does not arise from a chance neglect of investi-
gation of these relations. We cannot say that tomorrow, or
whenever we wish to take time, we can investigate these prob-
lems. On the contrary this inability is inherent in the nature
of the questions themselves. Although the conceptions in ques-
tion— namely, degrees of forgetfulness, of certainty and interest
— are quite correct, we have no means for establishing such
degrees in our experience except at the extremes, and even then
we cannot accurately limit those extremes. We feel therefore
that we are not at all in a condition to undertake the investiga-
tion. We form certain conceptions during striking experiences,
but we cannot find any realisation of them in the similar but less
striking experiences of everyday life. Vice versa there are prob-~
ably many conceptions which we have not as yet formed which
would be serviceable and indispensable for a clear understanding
of the facts, and their theoretical mastery.
The amount of detailed information which an individual has
at his command and his theoretical elaborations of the same
are rnutually_ ,dep_endent ; they grow in and through each other.
It is because of the indefinite and little specialised character
of our knowledge that the theories concerning the processes of
memory, reproduction, and association have been up to the
present time of so little value for a proper comprehension of
those processes. For example, to express our ideas concerning
their physical basis we use different metaphors — stored up ideas,
engraved images, well-beaten paths. There is only one thing
certain about these figures of speech and that is that they are
not suitable.
Of course the existence of all these deficiencies has its per-
fectly sufficient basis in the extraordinary difficulty and com-
plexity of the matter. It remains to be proved whether, in spite
6 Memory
of the clearest insight into the inadequacy of our knowledge,
we shall ever make any actual progress. Perhaps we shall
always have to be resigned to this. But a somewhat greater
accessibility than has so far been realised in this field cannot be
denied to it, as I hope to prove presently. If by any chance a
way to a deeper penetration into this matter should present itself,
surely, considering the significance of memory for all mental
phenomena, it should be our wish to enter that path at once.
For at the very worst we should prefer to see resignation arise
from the failure of earnest investigations rather than from
persistent, helpless astonishment in the face of their difficulties.
CHAPTER II
THE POSSIBILITY OF ENLARGING OUR KNOWL-
EDGE OF MEMORY
Section 4. The Method of Natural Science
ywA^ftC* ***•*
The ^method of obtaining exact measurements — i.e., numer-
ically exact ones — of the inner structure of causal relations -is,
by virtue of its nature, of general validity. This^R€thod,( indeed)
has been so exclusively used and so fully worked out by
the natural sciences that, as a rule, it is defined as something
peculiar to them, as the method of natural science. To repeat,
however, its logical nature makes it generally applicable to all
spheres of existence and phenomena. Moreover, the possibility
of defining accurately and exactly the actual behavior of any
process whatever, and thereby of giving a reliable basis for the
direct comprehension of its connections depends above all upon
the possibility of applying this method.
We all know of what this method consists: an attempt is
«f\ 6/*\ 'I
J /
.
of these conditions~IT Isolated from the rest and jrarted: in a CJT*~
way that can be numerically described; then the accompanying
change on the side of the effect is ascertained by measurement
or computation.
• Two fundamental and insurmountable difficulties, seem, how-
ever, to oppose a transfer of this method to the investigation of
the causal relations of mental events in general and of those of
memory in particular. In the first place, how are we to keep
even approximately constant the bewildering mass of causal
conditions which, in so far as they are of mental nature, almost
completely elude our control, and which, moreover, are subject
to endless and incessant change? In the second place, by what
possible means are we to measure numerically the mental pro-
cesses which flit by so quickly and which on introspection are so
7
'I
J /
"
8 Memory
hard to analyse? I shall first discuss the second difficulty in
connection, of course, with memory, since that is our present
oncern.
Section 5. Introduction of Numerical Measurements for Memory
Contents
If we consider once more the conditions of retention and
reproduction mentioned above (§2), but now with regard to
the possibility of computation, we shall see that with two of
them, at least, a numerical determination and a numerical varia-
tion are possible. The different times which elapse between
[the first production and the reproduction of a series of ideas
can be measured and the repetitions necessary to make these
series reproducible can be counted. At first sight, however, there
seems to be nothing similar to this on the side of the effects.
Here there is only one alternative, a reproduction is either pos-
sible or it is not possible. It takes place or it does not take
place. Of course we take for granted that it may approach,
under different conditions, more or less near to actual
occurrence so that in its subliminal existence the series possesses
graded differences. But as long as we limit our observations
to that which, either by chance or at the call of our will, comes
out from this inner realm, all these differences are for us equally
non-existent.
By somewhat less dependence upon introspection we can, how-
ever, by indirect* means force these differences into the open.
A poem is learned by heart and then not again repeated. We
will suppose that after a half year it has been forgotten: no
effort of recollection is able to call it back again into conscious •
ness. At best only isolated fragments return. Suppose that
the poem is again learned by heart. It then becomes evident
that, although to all appearances totally forgotten, it still in a
certain sense exists and in a way to be effective. The second
learning requires noticeably less time or a noticeably smaller
umber of repetitions than the first. It also requires less time
or repetitions than would now be necessary to learn a similar
poem of the same length. In this difference in time and number
of repetitions we have evidently obtained a certain measure
for that inner energy which a half year after the first learning
still dwells in that orderly complex of ideas which make up the
Possibility of Enlarging Our Knowledge of Memory 9
poem. After a shorter time we should expect to find the dif-
ference greater; after a longer time we should expect to find
it less. If 'the first committing to memory is a very careful and
long continued one, the difference will be greater than if it
is desultory and soon abandoned.
In short, we have without doubt in these differences numerical
expressions for the difference between these subliminally per-
sistent series of ideas, differences which otherwise we would
have to take for granted and would not be able to demonstrate
by direct observation. Therewith we have gained possession
of something that is at least like that which we are seeking
in our attempt to get a foothold for the application of the
method of the natural sciences : namely, phenomena on the side
of the effects which are clearly ascertainable, which vary in
accordance with the variation of conditions, and which are
capable of numerical determination. Whether we possess in
them correct measures for these inner differences, and whether /
we can achieve through them correct conceptions as to the causal
relations into which this hidden mental life enters — these ques-'
tions cannot be answered a priori. Chemistry is just as little
able to determine a priori whether it is the electrical phenomena,
or the thermal, or some other accompaniment of the process of
chemical union, which gives it its correct measure of the effective
forces of chemical affinity. There is only one way to do this,
and that is to see whether it is possible to obtain, on the pre-
supposition of the correctness of such an hypothesis^ well classi-
fied, uncontradictory results, and correct anticipations of the
future.
Instead of the simple phenomenon — occurrence or non-occur-
rence of a reproduction — which admits of no numerical distinc-}
tion, I intend therefore to consider from the experimental
standpoint a more complicated, process as the effect, and I shall
observe and measure its changes as the conditions are variedU
By this I mean the artificial bringing about by an appropriate
number of repetitions of a reproduction which would not occur
of its own accord.
But in order to realise this experimentally, two conditions at
least must be fulfilled.
Tn the first place, it must be possible to define with . some
certainty the moment when the goal is reached — i.e., when the
r
Memory
process of learning by heart is completed. For if the process
of learning by heart is sometimes carried past that moment and
sometimes broken off before it, then part of the differences found
under the varying circumstances would be due to this in-
equality, and it would be incorrect to attribute it solely to inner
differences in the series of ideas. Consequently among the
different reproductions of, say, a poem, occurring during the
process of its memorisation, the experimenter must single out
one' asi especially characteristic, and be able to find it again with
practical accuracy.
__In the second place the presupposition must be allowed that
the number of repetitions by means of which, the other condi-
tions being unchanged, this characteristic reproduction is brought
about would be every time the same. For if this number,
under conditions otherwise equivalent, is now this and now that,
the differences arising from varied conditions lose, of course,
all significance for the critical evaluation of those varying
conditions.
Now, as far as the first condition is concerned, it is easily
fulfilled wherever you have what may properly be called learn-
ing by heart, as in the case of poems, series of words, tone-
sequences, and the like. Here, in general, as the number of
repetitions increases, reproduction is at first fragmentary and
halting; then it gains in certainty; and finally takes place
smoothly and without error. The first reproduction in which
this last result appears can not only be singled out as especially
characteristic, but can also be practically recognised. For con-
venience I will designate this briefly as the first possible repro-
duction.
The question now is: — Does this fulfill the second condition
mentioned above? Is the number of repetitions necessary to
bring about this reproduction always the same, the other con-
ditions being equivalent?
However, in this form, the question will be justly rejected
because it forces upon us, as if it were an evident supposition,
the real point in question, the very heart of the matter, and
admits of none but a misleading answer. Anyone will be ready
to admit without hesitation that this relation of dependence
will be the same if perfect equality of experimental conditions
is maintained. The much invoked freedom of the will, at least.
Possibility of Enlarging Our Knowledge of Memory 1 1
has hardly ever been misunderstood by anybody so far as to
come in here. But this theoretical constancy is of little value:
How shall I find it when the circumstances under which I am
actually forced to make my observations are never the same?
So I must rather ask: — Can I bring under my control the in-
evitably and ever fluctuating circumstances and equalise them
to such an extent that the constancy presumably existent in the
causal relations in question becomes visible and palpable to me?
Thus the discussion of the one difficulty which opposes an
exact examination of the causal relations in the mental sphere
has led us of itself to the other (§4). A numerical determinsT")
tion of the interdependent changes of cause and effect appears
indeed possibl/ if)only we can realise the necessary uniformity
of the significant conditions in the repetition of our experiments.
Section 6. The Possibility of Maintaining the Constancy of
Conditions Requisite for Research
He who considers the complicated processes of the higher
mental life or who is occupied with the still more complicated
phenomena of the state and of society will in general be inclined
to deny the possibility of keeping constant the conditions for
psychological experimentation. Nothing is more familiar to
us than the capriciousness of mental life which brings to nought
all foresight and calculation. Factors which are to the highest
degree determinative and to the same extent changeable, such
as mental vigor, interest in the subject, concentration of atten-"p>
tion, changes in the course of thought which have been brought
about by sudden fancies and resolves — all these are either not at
all under our control or are so only to an unsatisfactory extent. V
However, care must be taken not to ascribe too much, weight
to these views, correct in themselves, when dealing with fields
other than those of the processes by the observation of which
these views were obtained. All such unruly factors are of the
greatest importance for higher mental processes which occur
only by an especially favorable concurrence of circumstances.
The more lowly, commonplace, and constantly occurring pro-
cesses are not in the least withdrawn from their influence, but
we have it for the most part in our power, when it is a matter
of consequence, to make this influence only slightly disturbing.
Sensorial perception, for example, certainly occurs with greater
Memory
or less accuracy according to the degree of interest; it is con-
• stantly given other directions by the change of external stimuli
and by ideas. But, in spite of that, we are on the whole
sufficiently able to see a house just when we want to see it and
to receive practically the same picture of it ten times in suc-
cession in case no objective change has occurred.
There is nothing a priori absurd in the assumption that ordin-
l ary retention and reproduction, which, according to general
agreement, is ranked next to sensorial perception, should also
behave like it in this respect. Whether this is actually the
case or not, however, I say now as I said before, cannot be
decided in advance. Our present knowledge is much too frag-
mentary, too general, too largely obtained from the extraordin-
ary to enable us to reach a decision on this point by its aid ;
at must be reserved for experiments especially adapted to that
urpose. We must try in experimental fashion to keep as
constant as possible those circumstances whose influence on
retention and reproduction is known or suspected, and then
ascertain whether that is sufficient. The material must be so
hosen that decided differences of interest are, at least to all
ppearances, excluded; equality of attention may be promoted
iy preventing external disturbances; sudden fancies are not
Subject to control, but, on the whole, their disturbing effect is
limited to the moment, and will be of comparatively little account
[f the time of the experiment is extended, etc.
When, however, we have actually obtained in such manner
/ the greatest possible constancy of conditions attainable by us,
(^ jfnow are we to know whether this is sufficient for our purpose ?
When are the circumstances, which will certainly offer differ-
ences enough to keen observation, sufficiently constant? The
answer may be made : — When upon repetition of the experiment
the results remain constant. The latter statement seems simple
enough to be self-evident, but on closer approach to the matter
still another difficulty is encountered.
Section 7. Constant Averages
When shall the results obtained from repeated experiments
under circumstances as much alike as possible pass for constant
or sufficiently constant? Is it wheji one result has the same
Possibility of Enlarging Our Knowledge of Memory 1 3
value as the other or at Isast deviates so little' from it that the
difference in proportion to its own quantity and for our pur-
poses is of no account ?
Evidently not. That would be asking too much, and is not
necessarily obtained even by the natural sciences. Then, perhaps
it is when the avejrages from larger groups of experiments
exhibit the characteristics mentioned above?
Again evidently not. That would be asking too little. For,
if observation of processes that resemble each other from any
point of view are thrown together in sufficiently large numbers, 1
fairly constant mean values are almost everywhere obtained
which, nevertheless, possess little or no importance for the pur-
poses which we have here. The exact distance of two signal
poles, the position of a star at a certain hour, the expansion
of a metal for a certain increase of temperature, all the numer-
ous coefficients and other constants of physics and chemistry are
given us as average values which only approximate to a high
degree of constancy. On the other hand the number of suicides
in a certain month, the average length of life in a given place,
the number of teams and pedestrians per day at a certain street
corner, and the like, are also noticeably constant, each being an
average from large groups of observations. But both kinds of
numbers, which I shall temporarily denote as constants of natural
science and statistical constants, are, as everybody knows, con-
stant from different causes and with entirely different significance
for the knowledge of causal relations.
These differences can be formulated as follows: —
In the case of the constants of the natural sciences each indi-^>
vidual effect is produced by a combination of causes exactly x>
"~afike.j The individual values come out somewhat differently
because a certain number or" those causes do not always join
the combination with exactly the same values (e. g., there are
little errors in the adjustment and reading of the instruments,
irregularities in the texture or composition of the material ex-
amined or employed, etc.). However, experience teaches us that
this fluctuation of separate causes does not occur absolutely
irregularly but that as a rule it runs through or, rather, tries
out limited and comparatively small circles of values symmet-
rically distributed around a central value. If several cases are
brought together the effects of the separate deviations must more
1 4 Memory
and more compensate each other and thereby be swallowed up
in the central value around which they occur. And the final
result of combining the values will be approximately the same
as if the actually changeable causes had remained the same
not only conceptually but also numerically. Thus, the average
value is in these cases the adequate numerical representative of
a conceptually definite and well limited system of causal con-
nections; if one part of the system is varied, the accompanying
changes of the average value again give the correct measure
for the effect of those deviations on the total complex.
On the other hand, no matter from what point of view sta-
tistical constants may be considered it cannot be said of them
that each separate value has resulted from the combination of
causes which by themselves had fluctuated within tolerably
narrow limits and in symmetrical fashion. The separate effects
arise, rather, from an oftimes inextricable multiplicity of causal
combinations of very different sorts, which, to be sure, may
share numerous factors with each other, but which, taken ag a
whole, have no conceivable community and actually correspond
only in some one characteristic of the effects. That the value
of the separate factors must be very different is, so to say, self
evident. That, nevertheless, approximately constant values ap-
pear even here by the combining of large groups — this fact we
may make intelligible by saying that in equal and tolerably large
intervals of time or extents of space the separate causal com-
binations will be realised with approximately equal frequency;
we do this without doing more than to acknowledge as extant a
peculiar and marvellous arrangement of nature. Accordingly
these constant mean values represent no definite and separate
causal systems but combinations of such which are by no means
of themselves transparent. Therefore their changes upon varia-
tion of conditions afford no genuine measure of the effects of
these variations but only indications of them. They are of no
direct value for the setting up of numerically exact relations
of dependence but they are preparatory to this.
Let us now turn back to the question raised at the beginning
of this section. When may we consider that this equality of
conditions which we have striven to realise experimentally has
been attained ? The answer runs as follows : When the average
values of several observations are approximately constant and
Possibility of Enlarging Our Knowledge of Memory 1 5
when at the same time we may assume that the separate cases V
belong to the same causal system, whose elements, however, are
not limited to exclusively constant values, but may run through
small circles of numerical values symmetrical around a middle \
value.
Section 8. The Law of Errors
Our question, however, is not answered conclusively by the
statement just made. Suppose we had in some way found satis-
factorily constant mean values for some psychical process, how
would we go about it to learn whether we might or might not
assume a homogeneous causal condition, necessary for their
further utilisation ? 4 The physical scientist generally knows
beforehand that he will have to deal with a single causal com-
bination, the statistician knows that he has to deal with a mask
of them, ever inextricable despite all analysis. Both know this
from the elementary knowledge they already possess of the .
nature of the processes before they proceed with the more \
detailed investigations. Just as, a moment ago, the present
knowledge of psychology appeared to us too vague and unreli- I
able to be depended upon for decision about the possibility of
constant experimental conditions ; so now it may prove insufficient
to determine satisfactorily whether in a given case we have to >
deal with a homogeneous causal combination or a manifold of
them which chance to operate together. The question is, there-
fore, whether we may throw light on the nature of the causation
of the results we obtain under conditions as uniform as possible
by the help of some other criterion.
The answer must be: This cannot be done with absolute cer-
tainty, but can, nevertheless, be done with great probability.
Thus, a start has been made from presuppositions as similar as
possible to those by which physical constants have been obtained
and the consequences which flow from them have been investi-
gated. This has been done for the distribution of the single
values about the resulting central value and quite independently
of the actual concrete characteristics of the causes. Repeated
comparisons of these calculated values with actual observations
have shown that the similarity of the suppositions is indeed great
enough to lead to an agreement of the results. The outcome
of these speculations closely approximates to reality. It consists
1 6 Memory
in this, — that the grouping of a large number of separate values
that have arisen from causes of the same kind and with the
modifications repeatedly mentioned, may be correctly represented
by a mathematical formula, the so-called Law of Errors. This
is especially characterised by the fact that it contains but one
unknown quantity. This unknown quantity measures the relative
compactness of the distribution of the separate values around
their central tendency. It therefore changes according to the
kind of observation and is determined by calculation from the
separate values.
NOTE. For further information concerning this formula, which
is not here our concern, I must refer to the text-books on the
calculation of probabilities and on the theory of errors. For
readers unfamiliar with the latter a graphic explanation will
be more comprehensible than a statement and discussion of the
formula. Imagine a certain observation to be repeated 1,000
times. Each observation as such is represented by a space of
one square millimeter, and its numerical value, or rather its
deviation from the central value of the whole 1,000 observations,
by its position on the horizontal line p q of the adjoining
Figure I.
For every observation which exactly corresponds with the
central value one square millimeter is laid off on the vertical
line m n. For each observed value which deviates by one
unit from the central value upward one square millimeter is
laid off on a vertical line to right of m n and distant one
millimeter from it, etc. For every observed value which devi-
ates by x units above (or below) the central value, one sq.
mm. is placed on a vertical line distant from m n by x
mms., to the right (or left, for values below the central value).
When all the observations are arranged in this way the outer
contour of the figure may be so compacted that the projecting
corners of the separate squares are transformed into a sym-
metrical curve. If now the separate measures are of such a
sort that their central value may be considered as a constant as
conceived by physical science, the form of the resulting curve is
of the kind marked a and b in Fig. I. If the middle
value is a statistical constant, the curve may have any sort of
a form. (The curves a and b with the lines p q in-
clude in each case an area of 1,000 sq. mms. This is strictly the
case only with indefinite prolongation of the curves and the lines
P q, but these lines and curves finally approach each other so
closely that where the drawing breaks off only two or three sq.
mms. at each end of the curve are missing from the full number.)
Whether, for a certain group of observations, the curve has a
Possibility of Enlarging Our Knowledge of Memory 1 7
more steep or more flat form depends on the nature of those
observations. The more exact they are, the more will they pile
up around the central value; and the more infrequent the large
deviations, the steeper will the curve be and vice versa. For
the rest the law of formation of the curve is always the same.
Therefore, if a person, in the case of any specific combination
of observations, obtains any measure of the compactness of
distribution of the observations, he can survey the grouping of
the whole mass. He could state, for instance, how often a
deviation of a certain value occurs and how many deviations
fall between certain limits. Or — as I shall show in what follows
— he may state what amount of variation includes between itself-
and the central value a certain per cent of all the observed values.
The lines -f- w and —w of our figure, for instance, cut out
exactly the central half of the total space representing the obser-
vations. But in the case of the more exact observations of I b
they are only one half as far from m n as in i a. So the state-
ment of their relative distances gives also a measure of the
accuracy of the observations.
1 8 Memory
Therefore, it may be said: wherever a group of effects may
be considered as having originated each time from the same_
causal combination, which was subject each time only to so-
called accidental disturbances, then these values arrange them-
selves in accordance with the —law of errors."
However, the reverse of this proposition is not necessarily
true, namely, that wherever a distribution of values occurs
according to the law of errors the inference may be drawn
that this kind of causation has been at work. Why should
nature not occasionally be able to produce an analogous group-
ing in a more complicated way? In reality this seems only an
extremely rare occurrence. For among all the groups of num-
bers which in statistics are usually condensed into mean values
not one has as yet been found which originated without question
\ from a number of causal systems and also exhibited the arrange-
\ ment summarised by the " law of errors."1
Accordingly, this law may be used as a criterion, not an abso-
lutely safe one to be sure, but still a highly probable one, by
means of which to judge whether the approximately constant
mean values that may be obtained by any proceeding may be
employed experimentally as genuine constants of science. The
Law of Errors does not furnish sufficient conditions for such
a use but it does furnish one of the necessary ones. The final
explanation must depend upon the outcome of investigations to
the very foundations of which it furnishes a certain security.
That is why I applied the measure offered by it to answer our
still unanswered question: If the conditions are kept as much
alike as is possible, is the average number of repetitions, which
is necessary for learning similar series to the point of first
possible reproduction, a constant mean value in the natural
science sense? And I may anticipate by saying that in the case
investigated the answer has come out in the affirmative.
xThe numbers representing the births of boys and girls respectively, as
derived from the total number of births, are said to group themselves in
very close correspondence with the law of errors. But in this case it is
for this very reason probable that they arise from a homogeneous combi-
nation of physiological causes aiming so to speak at the creation of a well
determined relation. (See Lexis, Zur Theorie der Massenerscheinungen
in der menschlichen Gesellschaft, p. 64 and elsewhere )
Possibility of Enlarging Our Knowledge of Memory 19
Section p. Resume
Two fundamental difficulties arise in the way of the applica-
tion of the so-called Natural Science Method to the examination
of psychical processes:
(1) The constant flux and caprice of mental events do not
admit of the establishment of stable experimental conditions.
(2) Psychical processes offer no means for measurement or i
enumeration.
In the case of the special field of memory (learning, retention, f
reproduction) the second difficulty may be overcome to a certain
extent. Among the external conditions of these processes some" 7
are directly accessible to measurement (the time, the number of •
repetitions). They may be employed in getting numerical values
indirectlywhere that would not have been possible directly.
We must not wait until the series of ideas committed to memory ,
return to consciousness of themselves, but we must meet them
halfway and renew them to such an extent that they may.jus^ \
be reproduced without error. The work requisite for this uncTer •
certain conditions I take experimentally as a measure of the/
influence of these conditions ; the differences in the work which
appear with a change of conditions I interpret as a measure of
the influence of that change.
Whether the first difficulty, the establishment of stable experi-
mental conditions, may also be overcome satisfactorily cannot
be decided a priori. Experiments must be made under conditions
as far as possible the same, to see whether the results, which
will probably deviate from one another when taken separately,
will furnish constant mean values when collected to form larger
groups. However, taken by itself, this is not sufficient to enable
us to utilise such numerical results for the establishment of
numerical relations of dependence in the natural science sense.
Statistics is concerned with a great mass of constant mean
values that do not at all arise from the frequent repetition of
an ideally frequent occurrence and therefore cannot favor
further insight into it. Such is the great complexity of our
mental life that it is not possible to deny that constant mean
values, when obtained, are of the nature of such statistical con-
stants. To test that, I examine the distribution of the separate
numbers represented in an average value. If it corresponds
2O . Memory
to the distribution found everywhere in natural science, where
repeated observation of the -same occurrence furnishes different
separate values, I suppose — tentatively again — that the repeatedly
examined psychical process in question occurred each time under
conditions sufficiently similar for our purposes. This supposi-
tion is not compulsory, but is very probable. If it is wrong, *
the continuation of experimentation will presumably teach this
by itself: the questions put from different points ofvview will
lead to contradictory results.
Section 10. The Probable Error
The quantity which measures the compactness of the observed
values obtained in any given case and which makes the formula
which represents their distribution a definite one may, as has
already been stated, be chosen differently. I use the so-called
" probable error " (P.E.) — i.e., that deviation above and below
the mean value which is just as often exceeded by- the separate
values as not reached by them, and which, therefore, between
its positive and negative limits, includes just half of all the
observational results symmetrically arranged around the mean
value. As is evident from the definition these values can be
obtained from the results by simple enumeration; it is done
more accurately by a theoretically based calculation.
If now this calculation is tried out tentatively for any group
of observations, a grouping of these values according to the
" law of errors " is recognised by the fact that between the sub-
multiples and the multiples of the empirically calculated probable
error there are obtained as many separate measures symmetrically
arranged about a central value as the theory requires.
According to this out of 1,000 observations there should be:
Number of
Within the^ limits separate measured
± A P-E. 54
. ± * P.E. 89.5
± i P.E. 134
± iP.E. 264
± P.E. 500
± H P.E. 688
± 2 P.E. 823
± 2$ P.E. 908
± 3 P.E. 957
± 4 P.E. 993
Possibility of Enlarging Our Knowledge of Memory 2 1
If. this conformity exists in a sufficient degree, then the mere
statement of the probable error suffices to characterise the
arrangement of all the observed values, and at the same time its
quantity gives a serviceable measure for the compactness of the
distribution around the central value — i.e., for its exactness and
trustworthiness.
As we have spoken of the probable error of the separate . ,
observations, (P.E.0), so can we also speak of the probable error
of the measures of the central tendency, or mean values, (P.E.m ).
This describes in similar fashion the grouping which would
arise for the separate mean values -if the observation of the
same phenomenon were repeated very many times and each time
an equally great number of observations were combined into a
central value. It furnishe's a brief but sufficient characterisation 1
of the fluctuations of the mean values resulting from repeated f
observations, and along with it a measure of the security and the""^
trustworthiness of the results already found.
The P.E.m is accordingly in general included in what follows.
How it is found by calculation, again, cannot be explained here;
suffice it that what it means be clear. It tells us, then, that, on the
basis of the character of the total observations from which a'
mean value has ju"st been obtained, it may be expected with a
probability of i tq_j^ that the latter value departs from the
presumably correct average by not more at the most than the
amount of its probable error. By the presumably correct average
we mean that one which would have been obtained if the
observations had been indefinitely repeated. A Jarger deviation
than this becomes improbable in the mathematical sense — i.e.,
there is a greater probability against it than for it. And, as a
glance at the accompanying table shows us, the improbability of
larger deviations increases with extreme rapidity as their size
increases. The probability that the obtained average should
deviate from the true one by more than 2^2 times the probable
error is only 92 to 908, therefore about i/io; the probability
for its exceeding four times the probable error is \ery slight,
7 to 993 (i to 142).
CHAPTER III
THE METHOD OF INVESTIGATION
Section n. Series of Nonsense Syllables
In order to test practically, although only for a limited field,
a way of penetrating more deeply into memory processes — and
it is to these that the preceding considerations have been directed
— I have hit upon the following method.
Out of the simple consonants of the alphabet and our eleven
vowels and diphthongs all possible syllables of a certain sort were
constructed, a vowel sound being placed between two consonants.1
These syllables, about 2,300 in number, were mixed together
and then drawn out by chance and used to construct series of
different lengths, several of which each time formed the material
for a test.8
At the beginning a few rules were observed to prevent, in
the construction of the syllables, too immediate repetition of
similar sounds, but these were not strictly adhered to. Later
they were abandoned and the matter left to chance. The syllables
used each time were carefully laid aside till the whole number
had been used, then they were mixed together and used again.
The aim of the tests carried on with these syllable series was,
by means of repeated audible perusal of the separate series, to
so impress them that immediately afterwards they could volun-
tarily just be reproduced. This aim was considered attained
1 The vowel sounds employed were a, e, i, o, u, a, 6, ii, au, ei, eu. For
the beginning of the syllables the following consonants were employed :
b, d, f, g, h, j, k, 1, m, n, p, r, s, (= sz), t, w and in addition ch, sch,
soft s, and the French j (19 altogether) ; for the end of the syllables f, k,
1, m, n, p, r, s, (= sz) t, ch, sch (n altogether). For the final sound
fewer consonants were employed than for the initial sound, because a Ger-
man tongue even after several years practise in foreign languages does not
quite accustom itself to the correct pronunciation of the mediae at the end.
For the same reason I refrained from the use of other foreign sounds
although I tried at first to use them for the sake of enriching the material.
2 1 shall retain in what follows the designations employed above and
call a group of several syllable series or a single series a " test." A num-
ber of " tests " I shall speak of as a " test series " or a " group of tests."
22
Tlie Meilwd of Investigation 23
when, the initial syllable being given, a series could be recited
at the first attempt, without hesitation, at a certain rate, and
with the consciousness of being correct.
Section 12. Advantages of the Material
The nonsense material, just described, offers many advantages,
in part because of this very lack of meaning. First of all, it
is .relatively simple and relatively homogeneous. In the case of
the material nearest at hand, tiamelypoetry or prose, the content
is now narrative in style, now descriptive, or now reflective; it
contains now^ a phrase that is pathetic, now one that is humorous ;
its metaphors are sometimes beautiful, sometimes harsh; its
rhythm is sometimes smooth and sometimes rough. There is
thus brought into play a multiplicity of influences which change
without regularity and are therefore disturbing. Such are asso-
ciations which dart here and there, different degrees of interest,
lines of verse recalled because of their striking quality or their
beauty, and the like. ^All this is avoided with our syllables^ -
Among many thousand combinations there occur scarcely a few
TfozerTthat have a meaning and among these there are again
only a few whose meaning was realised while they were being
memorised.
However, the simplicity and homogeneity of the material must
not be overestimated. It is still far from ideal. The learning
of the syllables calls into play the three sensory fields, sight, t
hearing and the muscle sense of the organs of speech. And !
although the part that each of these senses plays is well limited
and always similar in kind, a certain complication of the results
must still be anticipated because of their combined action. Again,
to particularise, the homogeneity of the series of syllables falls
considerably short of what might be expected of it. These series, \
exhibit very important and almost incomprehensible variations
as to the ease or difficulty with which they are learned. It even
appears from this point of view as if the differences between
sense and nonsense material were not nearly so great as one
would be inclined a priori to imagine. At least I found in the
case of learning by heart a few cantos from Byron's " Don
Juan " no greater range of distribution of the separate numerfcal
measures than in the case of a series of nonsense syllables in ]
24 Memory
the learning of which an approximately equal time had been
spent. In the former case the innumerable disturbing influences
mentioned above seem to have compensated each other in pro-
ducing a certain intermediate effect; whereas in the latter case
the predisposition, due to the influence of the^ mother tongue,
for certain combinations of letters and syllables must be a very
heterogeneous one.
More indubitable are the advantages of our material in two
other respects. In the. first place it permits an inexhaustible
amount of new combinations of quite homogeneous character,
while different poems, different prose pieces always have some-
thing incomparable. , It also makes possible a quantitative
variation which is adequate and certain ; whereas to break
off before the end or to begin in the middle of the verse or
the sentence leads to new complications because of various and
unavoidable disturbances of the meaning.
-.Series of numbers, which I also tried, appeared impracticable
for the more thorough tests. Their fundamental elements were
too small in number and therefore too easily exhausted.
Section 15. Establishment of the Most Constant Experimental
Conditions Possible
The following rules were made for the process of memorising.
/T) i. The separate series were always read through completely
L from beginning to end ; they were not learneBnrTseparate^arts
which were then joined together; neither were especially diffi-
cult parts detached and repeated more frequently! There was
a perfectly free interchange between the reading and the occa-
sionally necessary tests of the capacity to reproduce by heart.
• the latter there was an important rule to the effect that
upon hesitation the rest of the series was to be read through
to the end before beginning it again.
2. The rejidingjind the recitation of the series took place_at^
a ^onstanl_rate, that of 150 strokes per minute. A clockwork
metronome placed at some distance was at first used to regulate
the rate; but very soon the ticking of a watch was substituted,
that being much simpler and less disturbing to the attention.
The mechanism of escapement of most watches swings 300 times
per minute.
.
The Method of Investigation 25
3. Since it is practically impossible to speak continuously with-
out variation of accent, the following method was adopted to
avoid irregular variations: either three or four syllables were
united into a measure, and thus either the ist, 4th, 7th, or the
ist, 5th, Qth . . . syllables were pronounced with a slight
accent. Stressing of the voice was otherwise, as far as possible,
avoided.
4. After the learning of each separate series a pause of 15
seconds was made, and used for the tabulation of results. Then
the following series of the same test was immediately taken up.
5. During the process of learning, the purpose of reaching the
desired goal as soon as possible was kept in mind as much as
was feasible. Thus, to the limited degree to which conscious
resolve is of influence here, the attempt was made to keep the
attention concentrated on the tiresome task and its purpose. It
goes without saying that care was taken to keep away all outer
disturbances in order to make possible the attainment of this
aim. The smaller distractions caused by carrying on the test in
various surroundings were also avoided as far as that could
be done.
6. There was no attempt to connect the nonsense syllables by
the invention of special associations of the mnemotechnik
learning was carried on solely by the influence of the mere repe-
titions upon the natural memory. As I do not possess the least
practical knowledge of the mnemotechnical devices, the fulfill-
ment of this condition offered no difficulty to me.
7. Finally and chiefly, care was taken that the objective condi-
tions of life during the period of the tests were so controlled
as to eliminate too great changes or irregularities. Of course,
since the tests extended over many months, this was possible |
only to a limited extent. But, even so, the attempt was made
to conduct, under as similar conditions of life as possible, those
tests the results of which were to be directly compared. In
particular the activity immediately preceding the test was kept
as constant in character as was possible. Since the mental as
well as the physical condition of man is subject to an evident
periodicity of 24 hours, it was taken for granted that like experi-
mental conditions are obtainable only at like times of day^.
However, in order to carry out more than one test in a given
day, different experiments were occasionally carried on together
z6 Memory
at different times of day. When too great changes in the outer
and inner life occurred, the tests were discontinued for a length
of time. Their resumption was preceded by some days of re-
newed training varying according to the length of the inter-
ruption.
Section 14. Sources of Error
The guiding, point of view in the selection of material and
in determining the rules for its employment was, as is evident,
the attempt to simplify as far as possible, and to keep as constant
as possible, the conditions under which the activity to be
observed, that of memory, came into play. Naturally the better
one succeeds in this attempt the more does he withdraw from
the complicated and changing conditions under which this activity
takes place in ordinary life and under which it is of importance
to us. But that is no objection to the method. The freely
falling body and the f rictionless machine, etc., with which physics
deals, are also only abstractions when compared with the actual
happenings in nature which are of import to us. We can almost
nowhere get a direct knowledge of the complicated and the real,
but must get at them in roundabout ways by successive com-
binations of experiences, each of which is obtained in artificial,
\Nl experimental cases, rarely or never furnished in this form by
nature.
Meanwhile the fact that the connection with the activity of
memory in ordinary life is for the moment lost is of less im-
I portance than the reverse, namely, that this connection with the
1 complications and fluctuations of life is necessarily still a too
Lclose. one... The struggle to attain the most simple and uniform
conditions possible at numerous points naturally encounters
obstacles that are rooted in the nature of the case and which
thwart the attempt. The unavoidable dissimilarity of the
material and the equally unavoidable irregularity of the external
conditions have already been touched upon. I pass next to two
other unsurmountable sources of difficulty.
By means of the successive repetitions the series are, so to
speak, raised to ever higher levels. The natural assumption-
would be that at the moment when they could for the first time
be reproduced by heart the level thus attained would always be
the same. If only this were the case, i.e., if this characteristic
The Method of Investigation 2 7
first reproduction were everywhere an invariable objective sign of
an equally invariable fixedness of the series, it would be of real
value to us. This, however, is not actually the case. The inner
conditions of the separate series at the moment of the first
possible reproduction are not always the same, and the most that •
can be assumed is that in the case of these different series these
conditions always oscillate about the same degree of inner/
surety. This is clearly seen if the learning and repeating of
the series is continued after that first spontaneous reproduction
of the series has been attained. As a general thing the capacity
for^vohmtary reproduction persists after it has once been
reached. In numerous cases, however, it disappears immediately
after its first appearance, and is regained only after several
further repetitions. This proves that the predisposition for
memorising the series, irrespective of their differences of a
larger sort according to the time of day, to the objective and
subjective conditions, etc., is subject to small variations of short
duration, whether they be called oscillations of attention or some-
thing else. If, at the very instant when the material to be
memorised has almost reached the desired degree of surety, a
chance moment of especial mental clearness occurs, then the \
series is caught on the wing as it were, often to the learner's
surprise; but the series cannot long be retained. By the occur-
rence of a moment of special dullness, on the other hand,
first errorless reproduction is postponed for a while, although the
learner feels that he really is master of the thing and wonders
at the constantly recurring hesitations. In the former case, in
spite of the homogeneity of the external conditions, the first
errorless reproduction is reached at a point a little below the
level of retention normally connected with it. In the latter case
it is reached at a point a little above that level. As was said
before, the most plausible conjecture to make in this connection
is that these deviations will compensate each other in the case
of large groups.
Of the other source of error, I can only say that it may occur
and that, when it does, it is a source of great danger. I mean
the secret influence of theories and opinions which are in the
process of formation. An investigation usually starts out with
definite presuppositions as to what the results will be. But if
this is not the case at the start, such presuppositions form gradu-
a8 Memory
ally in case the experimenter is obliged to work alone. For it
/ js, impossible to carry on the investigations for any length of
time without taking notice of the results. The experimenter
must know whether the problem has been properly formulated
or whether it needs completion or correction. The fluctuations
of the results must be controlled in order that the separate
observations may be continued long enough to give to the mean
value the certainty necessary for the purpose in hand. Conse-
quently it is unavoidable that, after the observation of the
numerical results, suppositions should arise as to general prin-
ciples which are concealed in them and which occasionally give
hints as to their presence. As the investigations are carried
further, thesef suppositions, as' well as those present at the begin-
ning, constitute a complicating factor which probably has a
definite influence upon the subsequent results. It goes without
saying that what 1 have in mind is not any consciously recog-
nised influence but something similar to that which takes place
when one tries to be very unprejudiced or to rid one's self of
a thought and by that very attempt fosters that thought or
prejudice. The results are met half way with an anticipatory
knowledge, with a kind of expectation. Simply for the experi-
menter to say to himself that such anticipations must not be
allowed to alter the impartial character of the investigation will
not by itself bring about that result/ On the contrary, they do
lain and play a role in determining the whole inner attitude.
According as the subject notices that these anticipations are
confirmed or not confirmed (and in general he notices this dur-
ing the learning), he will feel, if only in a slight degree, a sort
of pleasure or surprise. And would you not expect that, in
spite of the greatest conscientiousness, the surprise felt by the
subject over especially startling deviations, whether positive or
negative, would result, without any volition on his part, in a
slight change of attitude? Would he not be likely to exert
himself a little more here and to relax a little more there than
would have been the case had he had no knowledge or presuppo-
sition concerning the probable numerical value of the results?
I cannot assert that this is always or even frequently the case,
since we are not here concerned with things that can be directly
observed, and since numerous results in which such secret warp-
ing of the truth might be expected show evident independence
The Method of Investigation 29
of it. All I can say is, we must expect something of the sort
from our general knowledge of human nature, and in any investi-
gations in which the inner attitude is of very great importance,
as for example in experiments on sense perception, we must
give special heed to its misleading influence.
It is evident how this influence in general makes itself felt.
With average values it would tend to level the extremes ; where
especially large or small numbers are expected it would tend to
further increase or decrease the values. This influence can
only be avoided with certainty when the tests are made by two
persons working together, one of whom acts as subject for a
certain time without raising any questions concerning the pur-
pose or the result of the investigations. Otherwise help can be
obtained only by roundabout methods, and then, probably, only
to a limited extent. The subject, as I myself always did, can
conceal from himself as long as possible the exact results. The
investigation can be extended in such a way that the upper limits
of the variables in question are attained. In this way, whatever
warping of the truth takes place becomes relatively more difficult
and unimportant. Finally, the subject can propose many prob-
lems which will appear to be independent of each other in the
hope that, as a result, the true relation of the interconnected
mental processes will break its way through.
To what extent the sources of error mentioned have affected
the results given below naturally cannot be exactly determined.
The absolute value of the numbers will doubtless be frequently
influenced by them, but as the purpose of the tests could never
have been the precise determination of absolute values, but
rather the attainment of comparative results (especially in the
numerical sense) and relatively still more general results, there
is no reason for too great anxiety. In one important case
(§ 38) I could directly convince myself that the exclusion
of all knowledge concerning the character of the results brought
about no change; in another case where I myself could not
eliminate a doubt I called especial attention to it. In any case
he who is inclined a priori to estimate very highly the uncon-
scious influence of secret wishes on the total mental attitude
will also have to take into consideration that the secret wish to
find objective truth and not with disproportionate toil to place
the creation of his own fancy upon feet of clay — that this wish,
30 Memory
I say, may also claim a place in the complicated mechanism of
these possible influences.
Section 15. Measurement of Work Required
Ur*-**
The number of repetitions which were necessary for memor-
ising a series up to the first possible reproduction was not
originally determined by counting, but indirectly by measuring
in seconds the time that was required to memorise it. My pur-
pose was in this way to avoid the distraction necessarily connected
with counting ; and I could assume that there was a proportional
relation existing between the times and the number of repetitions
occurring at any time in a definite rhythm. We could scarcely
expect this proportionality to be perfect, since, when only the
time is measured, the moments of hesitation and reflection are
included, which is not true when the repetitions are counted.
! Difficult series in which hesitation will occur relatively more
frequently, will, by the method of time measurement, get com-
paratively greater numbers, the easier series will get compara-
tively smaller numbers than when the repetitions are counted.
But with larger groups of series a tolerably equal distribution
of difficult and equal series may be taken for granted. Conse-
quently the deviations from proportionality will compensate
themselves in a similar manner in the case of each group.
When, for certain tests, the direct counting of the repetitions
became necessary, I proceeded in the following manner. Little
wooden buttons measuring about 14 mms. in diameter and 4
mms. at their greatest thickness were strung on a cord which
would permit of easy displacement and yet heavy enough to
prevent accidental slipping. Each tenth piece was black; the
others had their natural color. During the memorisation the
'cord was held in the hand and at each new repetition a piece
was displaced some centimeters from left to right. When the
series could be recited, a glance at the cord, since it was divided
into tens, was enough to ascertain the number of repetitions that
had been necessary. The manipulation required so little atten-
tion that in the mean values of the time used (which was always
tabulated at the same time) no lengthening could be noted as
compared with earlier tests.
By means of this simultaneous measurement of time and repe-
The Method of Investigation 3 1
titions incidental opportunity was afforded for verifying and
more accurately defining that which had been foreseen and
which has just been explained with regard to their interrelation.
When the prescribed rhythm of 150 strokes per minute was pre-
cis«ly maintained, each syllable would take 0.4 second ; and when
the simple reading of the series was interrupted by attempts
to recite it by heart, the unavoidable hesitations would lengthen
the time by small but fairly uniform amounts. This, however,
did not hold true with any exactness; on the contrary, the fol-
lowing modifications appeared.
Wlien the direct reading of the series predominated, a certain
forcing, an acceleration of the rhythm, occurred which, without | .
coming to consciousness, on the whole lowered the time for each
syllable below the standard of 0.4 sec.
When there was interchange between reading and reciting,
however, the lengthening of the time was not in general constant,
but was greater with the longer series. In this case, since the
difficulty increases very rapidly with increasing length of the
series, there occurs a slowing of the tempo, again involuntary
and not directly noticeable. Both are illustrated by the follow-
ing table. ,
Series of 16 syllables,
for the most part read
Each syllable required
the average time of
Number of
series
Number of
syllables
8 times
16 "
0.398 sec.
0.399 "
60
• 108
960
1728
Series
Were in part read,
Each syllable re-
Number
Number
of X
in part recited on
quired an average
of
of
syllables
an average Y times
time of Z sees.
series
syllables
X=
•y
Z=
12
18
0.416
63
756
16
31
0.427
252
4032
24
45
0.438
21
504
36
56
0.459
14
504
As soon as this direction of deviation from exact propor-
tionality was noticed there appeared in the learning a certain
conscious reaction against it. i
• •- •- ~~ — — — . |
3 a Memory
Finally, it appeared that the probable error of the time meas-
urements was somewhat larger than that of the repetitions.
' This relation is quite intelligible in the light of the explanations
given above. In the case of the time measurements the larger
values, which naturally occurred with the more difficult series,
' » -r •«*m~~-*m**
were relatively somewhat greater than in the case of the number
< of repetitions, because relatively they were for the most part
lengthened by the hesitations ; conversely, the smaller times were
necessarily somewhat smaller relatively than the number of
repetitions, because in general they corresponded to the easier
\ series. The distribution of the values in the case of the times
is therefore greater than that of the values in the case of the
repetitions.
The differences between the two methods of reckoning are,
as is readily seen, sufficiently large to lead to different results
in the case of investigations seeking a high degree of exactness.
rThat is not the case with the results as yet obtained ; it is there-
fore immaterial whether the number of seconds is used or that
of the repetitions.
Decision cannot be given a priori as to which method of
measurement is more correct — i.e., is the more adequate measure
of the mental work expended. It can be said that the im- \
pressions are due entirely to the repetitions, they are the thing ]
that counts ; it can be said that a hesitating repetition is just as
good as a simple fluent reproduction of the line, and that both-x
are to be counted equally. But on the other hand it may be
doubted that the moments of recollection are merely a loss.
In any case a certain display of energy takes place in them:
on the one hand, a very rapid additional recollection of the imme-
diately preceding words occurs, a new start, so to speak, to get
over the period of hesitation ; on the other hand, there is height-
ened attention to the passages following. If with this, as is
probable, a firmer memorisation of the series takes place, then
these moments have a claim upon consideration which can only
be given to them through the measurement of the times.
Only when a considerable difference in the results of the two
kinds of tabulation appears will it be possible to give one the
preference over the other. That one will then be chosen which
gives the simpler formulation of the results in question.
The Method of Investigation 3 3
Section 16. Periods of the Tests
The tests were made in two periods, in the years 1879-80 and
1883-84, and extended each over more than a year. During a
long time preliminary experiments of a similar nature had
preceded the definite tests of the first period, so that, for all
results communicated, the time of increasing skill may be con-
sidered as past. At the beginning of the second period I was
careful to give myself renewed training. This temporal distri-
bution of the tests with a separating interval of more than three
years gives the desired possibility of a certain mutual control
of most of the results. Frankly, the tests of the two periods
are not strictly comparable. In the case of the tests of the first
period, in order to limit the significance of the first fleeting grasp1^
of the series in moments of special concentration, it was decided
to study the series until two successive faultless reproductions
were possible. Later I abandoned this method, which only
incompletely accomplished its purpose, and kept to the first fluent
reproduction. The earlier method evidently in many cases re-
sulted in a somewhat longer period of learning. In addition
there was a difference in the hours of the day appointed for the
tests. Those of the later period all occurred in the afternoon
hours between one and three o'clock ; those of the earlier period
were unequally divided between the hours of 10-11 A. M., 11-12
A. M., and 6-8 P. M., which for the sake of brevity I shall desig- /
nate A, B, and C.
1 Described in § 14.
CHAPTER IV
THE UTILITY OF THE AVERAGES OBTAINED
Section if. Grouping of the Results of the Tests
The first question which awaits an answer from the investi-
gations carried out in the manner described is, as explained in
sections 7 and 8, that of the nature of the averages obtained.
Are the lengths of time required for memorising series of a
certain length, under conditions as nearly identical as possible,
grouped in such a way that we may be justified in considering
their average values as measures in the sense pf physical science,
or are they not?
If the tests are made in the way described above, namely,
so that several series are always memorised in immediate suc-
cession, such a type of grouping of the time records could
scarcely be expected. For, as the time devoted to learning at
a given sitting becomes extended, certain variable conditions
in the separate series come into play, the fluctuations of which
we could not very well expect, from what we know of their
.nature, to be distributed symmetrically around a mean value.
\ {Accordingly the grouping of the results must be an asymmetrical
''one and cannot correspond to the " law of error." Such con-
ditions are the fluctuations of attention and the decreasing mental
freshness, which, at first very quickly and then more and more
slowly, gives way to a certain mental fatigue. There are no
limits, so to speak, to the slowing down of the learning pro-
cesses caused by unusual distractions; as a result of these the
time for learning a series may occasionally be increased to
double that of its average value or more. The opposite effect,
that of an unusual exertion, cannot in the very nature of the
case overstep a certain limit. It can never reduce the learning
• itime to zero.
If, however, groups of series equal in number and learned in
immediate succession are taken, these disturbing influences
34
The Utility of tlrie Averages Obtained
35
may be considered to have disappeared or practically so.
The decrease in mental vigour in one group will be practically
the same as that in another. The positive and negative fluctua-
tions of attention which under like conditions occur during a
quarter or half hour are approximately the same from day to
day. All that is necessary to ask, then, is : Do the times neces^"
sary for learning equal groups of series exhibit the desired j
distribution ?
I can answer this question in the affirmative with sufficient
certainty. The two longest series, obtained under conditions
similar to each other, which I possess, are, to be sure, not large
in the abovermentioned theoretical sense; they suffer, moreover,
from the disadvantage that they originated at times separated
by comparatively long intervals during which there were neces-
sarily many changes in the conditions. In spite of this, their
grouping comes as near as could be expected to the one demanded
by the theory.
The first test series taken during the years 1879-80 comprises
92 tests. Each test consisted in memorising eight series of 13
syllables each, which process of learning was continued until
two reproductions of each series were possible. The time re-
quired for all eight series taken together including the time for
the two reproductions (but of course not for the pauses, see
p. 25, 4) amounted to an average of 1,112 seconds with
a probable error of observation of ± 76. The fluctuations of the
results were, therefore, very significant: only half of the nunv"^
bers obtained fell between the limits 1,036 and 1,188, the other1"'
half was distributed above and below these limits. In detail the
grouping of the numbers is as follows :
Number of deviations
limits
within the
By actual
Calculated
deviation
count
from theory
1 T> 17*
Tff "•&•
± 7
6
5
iP.E.
± 12
10
8.2
} P.E.
± 19
13
12.3
\ P E
± 38
30
24.3
P.E.
J- 76
45
46.0
U P.E.
± 114
61
63.4
2 P.E.
± 152
73
75.6
1\ P.E.
d- 190
84
83.6
3 P.E.
± 228
88
88.0
36 Memory
In the interval, y$ P.E. to y2 P.E., there occurs a slight piling
up of values which is compensated for by a greater lack in the
succeeding interval, y* P.E. to P.E. Apart from this, the corre-
spondence between the calculated and the actual results is satis-
factory. The symmetry of the distribution leaves something to
/ be desired. The values below the average preponderate a little
V in number, those above preponderate a little in amount of devia-
tion: only two of the largest eight deviations are below the
mean value. The influence of attention referred to above, the
fluctuations of which in the separate series show greater devia-
tions toward the upper limit than toward the lower, has not,
A A
therefore, been quite compensated by the combination of several
series.
The correctness of the observations and the correspondence
of their distributions with the one theoretically demanded are
greatly improved in the second large series of tests. The latter
comprises the results of 84 series of tests taken during the
years 1883-84. Each test consisted in memorising six series of
1 6 syllables each, carried on in each case to the first errorless
reproduction. The whole time necessary for this amounted to
1,261 seconds with the probable error of observation of ± 48.4 —
i.e., half of all the 84 numbers fell within the limits 1,213-1,309.
The exactness of the observations thus had greatly increased as
compared with the former series of tests:1
The interval included by the probable error amounts to only
7^/2 per cent of the mean value as against 14 per cent in the
earlier tests. In detail the numbers are distributed as follows:
1Of course, the exactness obtained here cannot stand comparison with
physical measurements, but it can very well be compared with physiolog-
ical ones, which would naturally be the first to be thought of in this con-
nection. To the most exact of physiological measurements belong the last
determinations of the speed of nervous transmission made by Helmhqltz
and Baxt. One record of these researches published as an illustration
of their accuracy (Mon. Ber. d. Berl. Akad. 1870, S. 191) after proper cal-
culation gives a mean value of 4.268 with the probable error of observa-
tion, o.ioi. The interval it includes amounts, therefore, to 5 per cent of
the mean value. All former determinations are much more inaccurate.
In the case of the most accurate test-series of the first measurements made
by Helmholtz, that interval amounts to about 50 per cent of the mean
value (Arch. f. Anat. u.. Physiol. 1850, S. 340). 'Even Physics, in the case
of its pioneer investigations, has often been obliged to put up with a less
degree of accuracy in its numerical results. In the case of his first deter-
minations of the mechanical equivalent of heat Joule found the number
838, with a probable error of observation of 97. (Phil. Mag., 1843, p.
435 ff.)
The Utility of the Averages Obtained
37
Number of deviations
Within the
limits
the
By actual
Calculated
deviation
count
from theory
^r P.E.
± 4
4
4.5
i P.E.
± 8
7
7.6
JP.E.
± 12
12
11 3
iP.E.
± 24
23
22.2
P.E.
± 48
44
42.0
li p JE.
± 72
57
57.8
2 P.E.
± 96
68
69.0
2^ P.E.
± 121
75
76.0
3 P.E.
± 145
81
80.0
1
The symmetry of distribution is here satisfactorily maintained
apart from the numbers, which are unimportant on account of
their smallness.
Deviations
limits
Above
Below
t P.E.
5
2
i P.E.
7
5
APE
13
10
P.E!
20
24
li P.E.
28
29
2 P.E.
34
34
2* P.E.
37
38.
3 P.E.
40
41
The deviation which is greatest absolutely is toward the lower
limit.
If several of our series of syllables were combined into groups
and then memorised separately, the length of time necessary to
memorise a whole group varied greatly, to be sure, when repeated
tests were taken; but, in spite of this, when taken as a whole
(they varied in a manner similar to that of the measures of the
ideally homogeneous processes of natural science, which also
vary from each other. So, at least in experimental fashion, it,
is allowable to use the mean values obtained from the numerical
results for the various tests in order to establish the existence
of causal relations just as natural science does that by means of
its constants.
The number of series of syllables which is to be combined into
Memory
a single group, or test, is naturally, .indeterminate.' It must be
expected, however, that as the number increases, the correspond-
ence between the distribution of the times actually found and
those calculated in accordance with the law of errors will be
greater. In practice the attempt will be made to increase the
number to such a point that further increase and the closer
correspondence resulting will no longer compensate for the time
required If the number of the series in a given test is lessened,
Jk€*aesired correspondence will also presumably decrease. How-
ever, it is desirable that even then the approximation to the
theoretically demanded distribution remain perceptible.
Even this requirement is fulfilled by the numerical values
obtained. In the two largest series of tests just described, I
have examined the varying length of time necessary for the
memorisation of the first half of each test. In the older series,
these are the periods required by each 4 series of syllables, in
the more recent series the periods required by each 3 of them
taken together. The results are as follows:
i. In the former series : mean value (ra)=533 (P.E.o)=±5i.
DISTRIBUTION OF THE SEPARATE VALUES
Within the
limits
i.e., within
the
deviation
Number of deviations
Of these deviations
there occur
By actual
count
Calculated
from theory
Below
Above
A P.E.
iP.E.
JP.E.
iP.E.
P.E.
1}P.E.
2 P.E.
2£ P.E.
3 P.E.
± 5
± 8
± 12
± 25
± 51
± 76
± 102
± 127
± 153
2
4
6
21
48
61
76
85
89
5.0
8.2
12.3
24.3
46.0
63.4
75.6
83.6
88.0
2
3
4
9
24
30
37
42
45
0
1
2
12
24
31
39
43
44
The Utility of the Averages Obtained
2. In the later series: w = 62o, P.E.0=±44.
DISTRIBUTION OF THE SEPARATE VALUES
39
Within the
limits
i.e., within
the
deviation
Number of deviations
Of these deviations
there occur
By actual
count
Calculated
from theory
Below
Above
1?i
iP.E.
*P.E.
W£P.E.
if P.E.
2 P.E.
2* P.E.
3 P.E.
± 4
± 7
± 11
± 22
± 44
± 66
± 88
± 110
± 132
3
5
11
25
44
56
71
76
79
4.5
7.6
11.3
22.2
42.0
57.8
69.0
76.0
80.0
1
3
6
13
21
29
38
41
42
2
2
5
12
23
27
33
35
37
By both tables the supposition mentioned above of the existence
of a less perfect but still perceptible correspondence between the
observed and calculated distribution of the numbers is well con-
firmed.
Exactly the same approximate correspondence must be pre-
supposed if, instead of decreasing the number of series combined
into a test, the total number of tests is made smaller. In this
case also I will add some confirmatory summaries.
I possess two long test series, made at the time of the earlier
tests, which were obtained under the same conditions as the
above mentioned series but at the later times of the day, B. and C.
One of these, B, comprised 39 tests of 6 series each, the other,
C, 38 tests of 8 series each, each series containing 13 syllables.
The results obtained were as follows :
40 Memory
i. For the tests at time B: w= 871, P.E.0= ± 63.
DISTRIBUTION OF THE SEPARATE VALUES
Within the
Number of deviations
1 * «"••»* 4 «
Counted
Calculated
1 P.E.
4
5
*P.E.
10
10.3
P.E.
21
19.5
li P.E.
28
26.8
2 P.E.
32
32.0
2£ P.E.
35
35.4
3 P.E.
37
37.3
2. For the tests of time C : m = 1,258, P.E.0= ± 60.
DISTRIBUTION OF THE SEPARATE VALUES
Within the
Number of deviations
uuuwa
Counted
Calculated
iP.E.
7
5.0
*P.E.
10
10.0
P.E.
19
19.0
1* P.E.
26
26.0
2 P.E.
31
31.0
2£ P.E.
34
34.5
3 P.E.
36
36.4
In addition I mention a^senesjDf only twentyjests, with which
I shall conclude this summary: Each test consisted of the
learning of eight separate series of thirteen syllables each, which
had been memorised once one month before. The average was
in this case 892 seconds with a probable error of observation of
54. The single values were grouped as follows:
Within the
Number of deviations
Counted
Calculated
1 P.E.
3
2.7
*P.E.
5
5.3
P.E.
10
10.0
H p-E.
12
13.8
2 P.E.
17
16.5
2£ P.E.
19
18.2
3 P.E.
20
19.1
The Utility of the Averages Obtained 41
Although the number of the tests was so small, the accordance
between the calculation by theory and the actual count of devia-
tions is in all these cases so close that the usefulness of the mean
values will be admitted, the wide limits of error being, of course,
taken into consideration.
Section 18. Grouping of the Results of the Separate Series
The previously mentioned hypotheses concerning the grouping
of the times necessary for learning the separate series were
naturally not merely theoretical suppositions, but had already
been confirmed by the groupings actually found. The two large
series of tests mentioned above, one consisting of 92 tests of
eight single series each, and the other of 84 tests of 6 single
series each, thus giving 736 and 504 separate values respectively,
afford a sufficiently broad basis for judgment. Both groups of
numbers, and both in the same way, show the following
peculiarities :
1. The distribution of the arithmetical values above their mean
is considerably looser and extends farther than below the mean.
The most extreme values above lie 2 times and 1.8 times, re-
spectively, as far from the mean as the most distant of those
below.
2. As a result of this dominance by the higher numbers the
mean is displaced upward from the region of the densest dis-
tribution, and as a result the deviations below get the preponder-
ance in number. There occur respectively 404 and 266 deviations
below as against 329 and 230 above.
3. The number of deviations from the region of densest dis-
tribution towards both limits does not decrease uniformly — as
one would be very much inclined to expect from the relatively
large numbers combined — but several maxima and minima of
density are distinctly noticeable. Therefore constant sources of
error were at work in the production of the separate values —
~fc?.", in the memorisation of the separate series. These resulted
on the one hand in an unsymmetrical distribution of the num-
bers, and on the other hand in an accumulation of them in certain
regions. In accordance with the investigations already presented
in this chapter, it can only be supposed that these influences com-
pensated each other when the values of several series learned in
succession were combined.
Memory
I have already mentioned as the probable cause of this unsym-
metrical distribution the peculiar variations in the effect of high
degrees of concentration of attention and distraction. It would
naturally be supposed that the position of the separate series
within each test is the cause of the repeated piling up of values
on each side of the average. If, in the case of a large test-series,
the values are summed up for the first, the second, and third
series, etc., and the average of each is taken, these average values
vary greatly, as might be expected. The separate values are
grouped about their mean with only tolerable approximation
to the law of error, but yet they are, on the whole, distributed
most densely in its region, and these separate regions of dense
distribution must of course appear in the total result.
MO c-
140
I H 777 jy y ~yj ~&H ~SHT
The following may be added by way of supplement : on account
of the mental fatigue which increases gradually during the course
of a test-series the mean values ought to increase with the num-
ber of the series ; but this does not prove to be the case.
Only in one case have I been able to notice anything corre-
sponding to this hypothesis, namely, in the large and therefore
important series of 92 tests consisting of eight series of 13
syllables each. In this case the mean values for the learning
of the 92 first series, the 92 second series, etc., were found to
be 105, 140, 142, 146, 146, 148, 144, 140 seconds, the relative
lengths of which Fig. 2 exhibits. For all the rest of the cases
which I investigated the typical fact is, on the contrary, rather
such a course of the numbers as was true in the case of the
The Utility of the Averages Obtained
43
series of 84 tests of six series of 16 syllables each and as is
shown in Fig. 3.
The mean values here were 191, 224, 206, 218, 210, 213 sec-
onds. They start in, as may be seen, considerably below the
average, but rise immediately to a height which is not again
reached in the further course of the test, and they then oscillate
220
210
zoo
790 1
m a
rather decidedly. An analogous course is shown by the numbers
in the 7 tests of nine 12-syllable series, namely: 71, 90, 98, 87,
98, 90, ioi, 86, 69 (Fig. 4).
m
Furthermore the values for 39 tests of six series of 13 syllables
each obtained in time B were as follows: 118, 150, 158, 147, 155,
144 (Fig. 5 lower curve).
Those for 38 tests with eight 13 syllable series of time C were
139. 159, 167, 168, 160, 150, 162, 153 (Fig. 5 upper curve).
Finally the numbers obtained from seven tests with six stanzas
of Byron's "Don Juan" were: 189, 219, 171, 204, 183, 229.
44
Memory
Even in the case of the first mentioned contradictory group
of tests J3. grouping of the separate mean values harmonising with
the normal one occurs if, instead of all the 92 tests being taken
into consideration at once, they are divided into several parts —
i.e., if tests are combined which were taken at about the same
time and under about the same conditions.
The conclusion cannot be drawn from these numerical results
that the mental fatigue which gradually increased during the
twenty minute duration of the tests did not exert any influence.
It can only be said that the supposed influence of the latter
upon the numbers is far outweighed by another tendency which
160
ISO
would not a priori be so readily suspected, namely the tendency
of comparatively low values to be followed by comparatively high
ones and vice versa. There seems to exist a kind of periodical
oscillation of mental receptivity or attention in ^OTm"ection~wfth
which the increasing fatigue expresses itself by fluctuations
around a median position which is gradually displaced.1
1 If it should ever become a matter of interest, the attempt might be
made to define numerically the different effects of that tendency in differ-
ent cases. For the probable errors of observation for the numerical
values of series-groups afford a measure for the influence of accidental
disturbances to which the memorisation is daily exposed. If now the
learning of the separate series in general were exposed to the same or
similar variations of condition as occur from test to test, then according
to the fundamental principles of the theory of errors, a probable error of
observation calculated directly from the separate values would relate itself
to the one just mentioned as I to v"rT, where " n " denotes the number of
separate series combined into a test. If, however, as is the case here,
special influences assert themselves during the memorisation of these
The Utility of the Averages Obtained 45
After orienting ourselves thus concerning the nature and value
of the numerical results gained from the complete memorisa-
tions, we shall now turn to the real purpose of the investigation,
namely the numerical description of causal relations.
separate series, and if such influences tend to separate the values further
than other variations of conditions would do, the " P.E.0 " calculated from
the separate values must turn out somewhat too great, and the just men-
tioned proportion consequently too small, and the stronger the influences
are, the more must this be the case.
An examination of the actual relations is, to be sure, a little difficult,
but fully confirms the statements. In the 84 tests, consisting of six series
of 16 syllables each, the Vn":=2.45. We found 48.4 to be the probable
error of observation of the 84 tests. The probable error of the 504 sep-
arate values is 31.6. The quotient 31.6: 48.4 is 1.53; therefore not quite
2/3 of the value of VrT.
CHAPTER V
RAPIDITY OF LEARNING SERIES OF SYLLABLES
AS A FUNCTION OF THEIR LENGTH
Section ip. Tests Belonging to the Later Period
I It is sufficiently well known that the memorisation of a series
of ideas that is to be reproduced at a later time is more difficult,
the longer the series is. That is, the memorisation not only
requires more time taken by itself, because each repetition lasts
i longer, but it also requires more time relatively because an in-
creased number of repetitions becomes necessary. Six verses
of a poem require for learning not only three times as much
time as two but considerably more than that.
I did not investigate especially this relation of dependence,
which of course becomes evident also in the first possible repro-
duction of series of nonsense syllables, but incidentally I ob-
tained a few numerical values for it which are worth putting
down, although they do not show particularly interesting
relations.
The series in question comprised (in the case of the tests of
the year 1883-84), 12, 16, 24, or 36 syllables each, and
9, 6, 3, or 2 series were each time com-
bined into a test.
For the number of repetitions necessary in these cases to
memorise the series up to the first errorless reproduction (and
including it) the following numerical results were found:
Required together
Probable error
Number
X series
Y syllables
an average of
of
of
each
Z repetitions
average values
tests
i
X=
Y —
z= n.iv. <
9
12
158
± 3.4
7
6
16
C ) 186
± 0.9
42
3
24
134. £/ fa
± 2.9
7
2
36
? |-TI2 & y
± 4.0
7
46
Rapidity of Learning Series of Syllables 47
In order to make the number of repetitions comparable it is
necessary, so to speak, to reduce them to a common denominator ^ -
and to divide them each time by the number of the series. In
this way it is found out how many repetitions relatively were
necessary to learn by heart the single series, which differ from
each other only in the number of syllables, and which each
time had been taken together with as many others of the same
kind as would make the duration of the whole test from fifteen
to thirty minutes.1
However, a conclusion can be drawn from the figures from the
standpoint of decrease in number of syllables. The question can
be asked : xtWhat number of syllables can be correctly recited
after only one reading? ^For me the number is usually seven.
Indeed I have often succeeded in reproducing eight syllables, but
this has happened only at the beginning of the tests and in a
decided minority of the cases. In the case of six syllables on
the other hand a mistake almost never occurs ; with them, there-
fore, a single attentive reading involves an unnecessarily large
expenditure of energy for an immediately following reproduction.1
If this latter pair of values is added, the required division
made, and the last faultless reproduction subtracted as not
necessary for the learning, then the following table results.
t -U^iAv *!
Number of repetitions
Number of necessary for first Probable
syllables errorless reproduction error
in a series (exclusive of it)
12 16.6 ±1.1
16 ,' 30.0 ±0.4
24 I 44.0 ± 1.7
36 ' 55.0 ± 2.8
'The objection might be made that, by means of this division, recourse
is made directly to the averages for the memorising of the single series,
and that in this way the result of the Fourth Chapter is disregarded. For,
according to that, the averages of the numbers obtained from groups of
series could indeed be used for investigation into relations of dependence,
but the averages obtained from separate series could not be so used. ^ I do
not claim, however, that the above numbers, thus obtained by division,
form the correct average for the numbers belonging to the separate series,
i.e., that the latter group themselves according to the law of errors. But
the numbers are to be considered as averages for groups of series, and, for
the sake of a better comparison with others — a condition which in the
nature of the case could not be everywhere the same — is made the same
by division. The probable error, the measure of their_ accuracy, has not
been calculated from the numbers for the separate series but from those
for the groups of series.
48 Memory
The longer of the two adjoining curves of Fig. 6 illustrates
the regular course of these numbers with approximate accuracy
for such a small number of tests. As Fig. 6 shows, in the cases
examined, the number of repetitions necessary for the memorisa-
tion of series in which the number of syllables progressively
increased, itself increases with extraordinary rapidity with the
increase in number of the syllables.
At first the ascent of the curve is very steep, but later on it
appears to gradually flatten out. For the mastery of five times
JO
^o
JO
—rig.6-
it-fir/Mmiliiiiliiiiliiiiliiiilinil
0 ' 10 40
the number of syllables that can be reproduced after but one
reading — i.e., after about 3 seconds — over 50 repetitions were
necessary, requiring an uninterrupted and concentrated effort
for fifteen minutes.
The curve has its natural starting point in the zero point of
the co-ordinates. The short initial stretch up to the point,
x — 7> y — J> can be explained thus: in order to recite by heart
series of 6, 5, 4, etc., syllables one reading, of course, is all that
is necessary. In my case this reading does not require as
much attention as does the /-syllable one, but can become more
and more superficial as the number of syllables decreases.
Rapidity of Learning Series of Syllables
49
Section 20. Tests Belonging to the Earlier Period
It goes without saying that since the results reported were
obtained from only one person they have meaning only as related
to him. The question arises whether they are for this individual
of a general significance — i.e., whether, by repetition of the tests
at another time, they could be expected to show approximately
the same amount and grouping.
A series of results from the earlier period furnishes the de-
sired possibility of a control in this direction. They, again,
have been obtained incidentally (consequently uninfluenced by
expectations and suppositions) and from tests made under dif-
ferent conditions than those mentioned. These earlier tests
occurred at an earlier hour of the day and the learning was
continued until the separate series could be recited twice in
succession without mistake. A test comprised
15 series of 10 syllables each,
or 8 " " 13
or 6 " " 16
or 4 " " 19
So, again, four different lengths of series have been taken
into account, but their separate values lie much closer together.
Since the repetitions — which are in question here — were not
counted at all in the earlier period, their number had to be cal-
culated from the times. For this purpose the table on p. 31
has been used after corresponding interpolation. If the num-
bers found are immediately reduced to one series each, and if
along with it the two repetitions representing the recitation are
subtracted as above, we obtain :
Number of
syllables
in a series
Number of repetitions
necessary for two
errorless reproductions
(exclusive of them)
Probable
error1
Number
of tests
10
13
16
19
13
23
32
38
± 1.
± 0.5
± 1.2
± 2.0
16
92
6
11
1The probable errors are based upon calculation and have only an
approximate value.
50 Memory
The smaller curve of Fig. 6 exhibits graphically the arrange-
ment of these numbers. As may be seen, the number of repeti-
tions necessary for learning equally long series was a little larger
in the earlier period than in the later one. Because of its uni-
formity this relation is to be attributed to differences in the
experimental conditions, to inaccuracies in the calculations, and
perhaps also to the increased training of the later period. The
older numbers fall very close to the position of the later ones,
and — what is of chief importance — the two curves lie as closely
together throughout the short extent of their common course
as could be desired for tests separated by 3^ years and un-
affected by any presuppositions. There is a high degree of prob-
ability, then, in favor of the supposition that the relations of
dependence presented in those curves, since they remained con-
stant over a long interval of time, are to be considered as char-
acteristic for the person concerned, although they are, to be
sure, only individual.
Section 21. Increase in Rapidity of Learning in the Case of
Meaningful Material
In order to keep in mind the similarities and differences be-
tween sense and nonsense material, I occasionally made tests
with the English original of Byron's " Don Juan." These
results do not properly belong here since I did not vary the
length of the amount to be learned each time but memorised
on each occasion only separate stanzas. Nevertheless, it is in-
teresting to mention the number of repetitions necessary because
of their contrast with the numerical results just given.
There are only seven tests (1884) to be considered, each of
which comprised six stanzas. When the latter, each by itself,
were learned to the point of the first possible reproduction, an
average of 52 repetitions (P.E.m=-j-O.6) was necessary for all
six taken together. Thus, each stanza required hardly nine repe-
titions; or, if the errorless reproduction is abstracted, scarcely
eight repetitions.1
1 For the sake of correct evaluation of the numbers and correct connec-
tion with possible individual observations, please note p. 24, i.
In order to procure uniformity of method the stanzas were always
read through from beginning to end ; more difficult passages were not
learned separately and then inserted. If that had been done, the times
would have been much shorter and nothing could have been said about
Rapidity of Learning Series of Syllables 5 1
If it is born in mind that each stanza contains 80 syllables
(each syllable, however, consisting on the average of less than
three letters) and if the number of repetitions here found is
compared with the results presented above, there is obtained an
approximate numerical expression for the extraordinary advan- r'
tage which the combined ties of meaning, rhythm, rhyme,
a common language give to material to be memorised. If the
above curve is projected in imagination still further along its pres-
ent course, then it must be supposed that I would have required 70
to 80 repetitions for the memorisation of a series of 80 to 90
nonsense syllables. When the syllables were objectively and sub-"
jectively united by the ties just mentioned this requirement was / '
in my case reduced to about one-tenth of that amount.
the number of repetitions. Of course the reading was done at a uniform
rate of speed as far as possible, but not in the slow and mechanically
regulated time that was employed for the series of syllables. The regula-
tion of speed was left to free estimation. A single reading of one stanza
required 20 to 23 seconds.
CHAPTER VI
RETENTION AS A FUNCTION OF THE NUMBER OF
REPETITIONS
Section 22. Statement of the Problem
The result of the fourth chapter was as follows: When in
repeated cases I memorised series of syllables of a certain length
to the point of their first possible reproduction, the times, (or
number of repetitions) necessary differed greatly from each
other, but the mean values derived from them had the character
of genuine constants of natural science. Ordinarily, therefore,
I learned by heart homogeneous series under similar conditions
with, on the average, a similar number of repetitions.. The large
deviations of the separate values from each other/ change the
total result not at all; but it would require too much time to
ascertain with exactness the number necessary for greater pre-
cision in detail.
What will happen, it may be asked, if the number of repe-
titions actually given to a certain series is less than is required
for memorisation or if the number exceeds the necessary
minimum ?
The general nature of what happens has already been de-
scribed. Naturally the surplus repetitions of the latter alterna-
tive do not go to waste. Even though the immediate effect, the
smooth and errorless reproduction, is not affected by them, yet
they are not without significance in that they serve to make other
such reproductions possible at a more or less distant time. The
longer a person studies, the longer he retains. And, even in the
first case, something evidently occurs even if the repetitions do
V not suffice for a free reproduction. By them a way is at least
opened for the first errorless reproduction, and the disconnected,
hesitating, and faulty reproductions keep approximating more
and more to it,
These relations can be described figuratively by speaking of the
52
Retention as a Function of the Number of Repetitions 53
series as being more or less deeply engraved in some mental sub-
stratum. To carry out this figure: as the number of repetitions^
increases, the series are engraved more 'and more deeply and j
indelibly; if the number of repetitions is small, the inscription
is but surface deep and only fleeting glimpses of the tracery can
be caught ; with a somewhat greater number the inscription can,
for a time at least, be read at will ; as the number of repetitions
is still further increased, the deeply cut picture of the series
fades out only after ever longer intervals.
What is to be said in case a person is not satisfied with this
general statement of a relation of dependence between the num-
ber of repetitions and the depth of the mental impression ob-
tained, and if he demands that it be defined more clearly and
in detail? The thermometer rises with increasing temperature,
the magnetic needle is displaced to an increasing angle as the
intensity, of the electric current around it increases. But while
the mercury always rises by equal spaces for each equal increase
in temperature, the increase of the angle showing the displace-
ment of the magnetic needle becomes less with a like increase
in the electric current. Which analogy is it which holds for the
effect of the number of repetitions of the series to be memorised
upon the depth of the resulting impression? Without further
discussion shall we make it proportional to the number of repe-
titions, and accordingly say that it is twice or three times as
great when homogenous series are repeated with the same degree
of attention twice or thrice as many times as are others? Or
does it increase less and less with each and every constant increase
in the jmmber of repetitions? Or what does happen?
Evidently this question is a good one; its answer would be
of theoretical as well as practical interest and importance. But
with the resources hitherto at hand it could not be answered,
nor even investigated. Even its meaning will not be quite clear
so long as the words " inner stability " and " depth of impression "
denote something indefinite and figurative rather than something
clear and objectively defined.
Applying the principles developed in section 5, I define the
inner stability of a series of ideas— the^degree of its retainability
—by the greater or less readiness with which it is reproduced at
some definite time subsequent to its first memorisation. This
readiness I measure by the amount of work saved in the re-
54 Memory
learning, of any series as compared with the work necessary
for memorising a similar but entirely new series.
The interval of time between the two processes of memorisa-
tion is of course a matter of choice. I chose 24 hours.
Since in the case of this definition we are not trying to settle
a matter of general linguistic usage, it cannot be properly asked
whether it is correct, but only whether it serves the purpose,
or, at the most, whether it is applicable to the indefinite ideas
connected with the notion of different depths of mental im-
pression. The latter will probably be granted. But nothing can
be said in advance as to how well it fulfills its purpose. That
dan be judged only after more extensive results have been ob-
tained. And the character of the judgment will depend to a
great extent on whether the results obtained with the help of
this means of measurement fulfill the primary demand which
we make with reference to any system of measurement. It
consists in this, — that if any change whatever is made in the
controllable conditions of that scale, the results obtained
by the scale in its new form can be reduced to those of the old
form by multiplication by some one constant. In our present
case, for example, it would consequently be necessary to know
whether the character of the results would remain the same if
any other interval had been employed instead of that of 24 hours,
arbitrarily chosen for measuring the after-effect of repetitions,
or whether as a consequence the entire rationale of the results
would be different, just as the absolute values are necessarily
different. Naturally, this question cannot be decided a priori.
For ascertaining the relation of dependence between the in-
crease in the number of repetitions of a series and the ever
vjl deeper impression of it which results, I have formulated the
jMK1; problem as follows: If homogeneous series are impressed to
' A different extents as a result of different numbers of repetitions,
and then 24 hours later are learned to the point of the first
possible reproduction by heart, how are the resulting savings in
work related to each other and to the corresponding number of
former repetitions?
Section 23. The Tests and their Results
In order to answer the question just formulated, I have car-
ried out 70 double tests, each of six series of 16 syllables each.
Retention as a Function of the Number of Repetitions 55
Each double test consisted in this, that the separate series — each
for itself — were first read attentively a given number of times
(after frequently repeated readings they were recited by heart
instead of read), and that 24 hours later I relearned up to the
point of first possible reproduction the series thus impressed
and then in part forgotten. The first reading was repeated 8,
16, 24, 32, 42, 53, or 64 times.
An increase of the readings used for the first learning beyond
64 repetitions proved impracticable, at least for six series of this
length. For with this number each test requires about ^ of
an hour, and toward the end of this time exhaustion, headache,
aftd other symptoms were often felt which would have com-
plicated the conditions of the test if the number of repetitions
had been increased.
The tests were equally divided among the seven numbers of
repetitions investigated so that to each of them were allotted 10
double tests. The results were as follows for the six series of a
single test taken together and without subtraction of the time
used for reciting.
After a preceding study of the series by means of " x " repe-
titions, they were learned 24 hours later with an expenditure of
" y " seconds.
x = 8
x = 16
x = 24
x = 32
x = 42
x = 53
x = 64
y=
y=
y=
y=
y—
y=
V " • ~
1171
998
1013
736
708
615
530
1070
795
853
764
579
579
483
1204
' 936
v 854
863
734
601
499
1180
1124
908
850
660
561
464
1246
1168
1004
892
738
618
412
1113
1160
1068
868
713
582
419
1283
1189
979
913
649
572
417
1141
1186
966
858
634
516
397
1127
1164
1076
914
788
550
391
1139
1059
1033
975
763
660
524
m= 1167
1078
975
863
697
585
454
P.E.m=±14 ±28 ± 17 ± 15 ±14 ± 9 ± 11
The preceding table of numbers gives the timej_ac£MJ[Z3LJ4££flf '
in learning by heart the series studied 24 hours previously. Since
we are interested not so much in the times used as the times
saved, we must know how long it would have taken to learn by
heart the same series if no previous study had been made. In
the case of the series which were repeated 42, 53, and 64 times,
-
556
Memory
this time can be learned from the tests themselves. For, in
their case, the number of repetitions is greater than the average
ninimum for the first possible reproduction, which in the case
i>f the i6-syllable series (p. 46) amounted to 31 repe-
titions. In their case, therefore, the point can be determined
at which the first errorless reproduction of that series appeared
as the number of repetitions kept on increasing. But on account
of the continued increase in the number of repetitions and the
resulting extension of the time of the test, the conditions were
somewhat different from those in the customary learning of
series not hitherto studied. In the case of the series to which
a smaller number of repetitions than the above were given, the
numbers necessary for comparison cannot be derived from their
own records, since, as a part jaf the plan of the experiment, they
were not completely learned by heart. I have consequently pre-
ferred each time to find the saving of work in question by com-
parison with the time required for learning by heart not the
same but a similar series up to that time unknown. For this
I possess a fairly correct numerical value from the time of the
tests in question: any six i6-syllable series was learned, as an
average of 53 tests, in 1,270 seconds, with the small probable
error ± 7.
If all the mean values are brought together in relation to this
last value, the following table results:
I
II
III
IV
After a preceding
study of the
They were just
memorized 24
The result therefore
of the preceding
Or, for each of
the repetitions, an
series by X
repetitions,
hours later in
Y seconds
study was a saving
of T seconds,
average saving
of D seconds
X=
Y«
PIT1
.-Ej.m —
T=
P.E.m=
D=
7/ Sec*
0
1270
7
8
1167
14
103
16
12.9
10
1078
28
192
29
12.0
24
975
17
295
19
12.3
32^
863
15
407
17
12.7
42
697
14
573
. 16
13.6
53
585
9
685 3
11
12.9
64
454
11
816
13
12.8
m=12.7
Retention as a Function of the Number of Repeiitions 57
The simple relation approximately realised in these numbers
is evident : the number of repetitions used to impress the series
(Column I) and the saving in work in learning the series 24
hours later as a result of such impression (Col. III)Jincrease
in the same fashion. Division of the amount of work saved by
trie" corresponding number of repetitions gives as a quotient a
practically constant value (Col. IV).
Consequently the results of the test may be summarised and
formulated as follows: When nonsense series of 16 syllables each
were impressed in memory to greater and greater degrees by
means of attentive repetitions, the inner depth of impression
in part resulting from the number of the repetitions increased,
within certain limits, approximately proportionally to that num-
ber. This increase in depth was measured by the greater readi-
ness with which these series were brought to the point of repro-
duction after 24 hours. The limits within which this relation
was determined were on the one side, zero, and, on the other,
about double the number of repetitions that on the average
just sufficed for learning the series.
For six series taken together the after-effect of each repeti-
tion— i.e., the saving it brought about — amounted on the average
to 12.7 seconds, consequently to 2.1 seconds for each single
series. As the rejg^tijaQri of a series of 16 syllables Jn_itself
takes from 6.6 to 6.8 seconds, its after-effect 24 hours later
amounts to a scant third of its own duration. In other words:
for each three additional repetitions which I spent on a given day
on the study of a series, I saved, in learning that series 24 houri
later, on the average, approximately one repetition; and, within
the limits stated, it did not matter how many repetitions alto-,;
gether were spent on the memorisation of a series.
Whether the results found can claim any more general impor-
tance, or whether they hold good only for the single time of
their actual occurrence, and even then give a false im-
pression of a regularity not otherwise present, I cannot now
decide. I have no direct control tests. Later, however, (chapter
VIII, § 34~)^where results obtained in reference to quite a
different problem agree with the present results, I can bring for-
ward indirect evidence on this point. I am therefore inclined to
58 Memory
ascribe general validity to these results, at least for my own
case.
NOTE. — There is in the tests an inner inequality which I can neither
avoid, nor remove by correction, but can only point out. It is that a
small number of repetitions of the series requires only a few minutes, and
consequently come at a time of unusual mental vitality. With 64 repeti-
tions the whole work takes about y$ of an hour ; the great part of the series
is, therefore, studied in»a condition of diminished vigor or even of a certain
exhaustion, and the repetitions will, consequently, be less effective. It
is just the reverse of this in the reproduction of the series the next
day. The series impressed by 8 perusals require three times as much
time in order to be memorised as those perused 64 times. Consequently
the latter will be learned a little more quickly not only on account of
their greater fixedness, but also because they are now studied for the
most part under better conditions. These irregularities are mutually
opposed, as is evident, and therefore partially compensate each other :
the series prepared under comparatively unfavorable conditions ire
memorised under comparatively more favorable conditions, and vice
versa. I cannot tell, however, how far this compensation goes and
how far any remaining inequality of conditions disturbs the results.
Section 24. The Influence of Recollection
One factor in the regular course of the results obtained seems
to deserve special attention. In ordinary life it is of the greatest
importance, as far as the form which memory assumes is con-
cerned, whether the reproductions occur with accompanying-
recollection or not, — i.e., whether the recurring ideas simply
return or whether a knowledge of their former existence and cir-
cumstances comes back with them. For, in this second case, they
obtain a higher and special value for our practical aims and
for the manifestations of higher mental life. The question now
is, what connection is there between the inner life of these ideas
and the complicated phenomena of recollection which sometimes
do and sometimes do not accompany the appearance in con-
sciousness of images? Our results contribute somewhat toward
the answer to this question.
When the series were repeated 8 or 16 times they had become
I unfamiliar to me by the next day. Of course, indirectly, I knew
quite well that they must be the same as the ones studied the
day before, but I knew this only indirectly. I did not get it from
the series, I did not recognise them. But with 53 or 64 repeti-
tions I soon, if not immediately, treated them as old acquaint-
ances, I remembered them distinctly. Nothing corresponding to
this difference is evident in the times for memorisation and for
savings of work respectively. They are not smaller relatively
Retention as a Function of the Number of Repetitions 59
when there is no possibility of recollection nor larger relatively
when recollection is sure and vivid. The regularity of the after-
effect of many repetitions does not noticeably deviate from the
line that is, so to speak, marked out by a smaller number of repe-
titions although the occurrence of this after-effect is accompanied
by recollection in the first case just as indubitably as it lacks '
recollection in the second case.
I restrict myself to pointing out this noteworthy fact. Gen-
eral conclusions from it would lack foundation as long as the
common cause cannot be proved.
Section 25. The Effect of a Decided Increase in the Number of
Repetitions
It would be of interest to know whether the approximate pro-
portionality between the number of repetitions of a series and ',
the saving of the work in relearning the latter made possible
thereby, which in my own case seemed to take place within
certain limits, continues to exist beyond those limits. If, further-
more, as a result of each repetition a scant third of its own
value is saved up to be applied on the reproduction 24 hours
later, I should be able to just reproduce spontaneously after 24
hours a series of 16 syllables, the initial syllable being given,
provided I had repeated it the first day thrice as many times
as were absolutely necessary for its first reproduction. As this
requirement is 31-32 repetitions the attainment of the aim in ques- ,
tion would necessitate about 100 repetitions. On the supposi-
tion of the general validity of the relation found, the number of
repetitions to be made at a given time, in order that errorless
reproduction might take place 24 hours later, could be calculated
for any kind of series for which, so to say, the " after-effect-
coefficient " of the repetitions had been ascertained.""
I have not investigated this question by further increasing the
number of repetitions of unfamiliar 16 syllable series because,
as has been already noted, with any great extension of the tests
the increasing fatigue and a certain drowsiness cause complica-
tions. However, I have made some trial tests partly with shorter
series, and partly with familiar series, all of which confirmed
the result that the proportion in question gradually ceases to hold
with a further increase of repetitions. Measured by the saving
6o
Memory
of work after 24 hours the effect of the later repetitions gradu-
ally decreases.
Series of 12 syllables (six of the series were each time
combined into a test) were studied to the point of first possible
reproduction; and immediately after the errorless reproduction
each series was repeated three times (in all four times) as often
as the memorisation (exclusive of the recital) had required.
After 24 hours the same series were relearned to the first possible
reproduction. Four tests furnished the following results (the
numbers indicate the repetitions) :
Repetitions
Immediately
Total
After 24
Thus the work
for the
successive
number of
hours the
saved by the
learning and
repetitions
repetitions
memorization
total number
recital of
for the sake of
used for the
of the series
of repetitions
6 series
greater surety
6 series
required
amounted to
104
294
398
41
63
101
285
386
39
62
114
324
438
46
68
109
309
.418
38
71
m= 107
303
410
41
66
P.E.m=1.4
In my own case — within reasonable limits — the after-effect
of the repetitions of series of 12 syllables after 24 hours is a
little smaller than is the case with 16 syllables; it must be
estimated as at least three tenths of the sum total of the repe-
titions. If this relation were approximately to continue to hold
with very numerous repetitions, it would be reasonable to expect
that, after 24 hours, series on whose impression four times as
many repetitions had been expended as were necessary for their
first reproduction could be recited without any further expendi-
ture of energy. Instead of this, in the cases examined, the re-
learning required about 35 per cent of the work required for
the first recital. The effect of an average number of 410 repe-
titions was a saving of only one sixth of this sum. If now
the first repetitions were represented by about three tenths of
their amount, the effect of the later repetitions must have been
very slight.
Investigations of the following kind, which I do not here
give in detail, led to the same result. Syllable series of different
Retention as a Function of the Number of Repetitions 61
lengths were gradually memorised by frequent repetitions which,
however, did not all take place on one day, but were distributed
over several successive days (Chap. VIII). When, after several
days, only a few repetitions were necessary in order to learn the
series by heart, they were repeated three or four times as often
as was necessary, at this phase of memorisation, for the first
errorless reproduction. But in no single case did I succee^m->v
an errorless reproduction of the series after 24 hours unless /
I had read them again once or several times. The influence of
the frequent repetitions still appeared, indeed, in a certain saving
of work, but this became less in proportion to the decreasing
amount of work to be saved. It was very hard, by means of
repetitions which had taken place 24 hours previously, to elimin- •
ate the last remnant of the work of relearning a given series.
To summarise: The effect of increasing the number of repe-
titions of series of syllables on their inner fixedness in the above
defined sense grew at first approximately in proportion to the
number of repetitions, then that effect decreased gradually, and
finally became very slight when the series were so deeply im-
pressed that they could be repeated after 24 hours, almost spon-
taneously. Since this decrease must be considered gradual and
continuous, its beginning would, in more accurate investigations,
probably have become evident even within the limits withhl which
we found a proportionality, whereas now it is hidden on account
of its small amount and the wide limits of error.
CHAPTER VII
RETENTION AND OBLIVISCENCE AS A FUNCTION
OF THE TIME
Section 26. Explanations of Retention and Obliviscence
All sorts of ideas, if left to themselves, are gradually for-
gotten. This fact is generally known. Groups or series of
ideas which at first we could easily recollect or which recurred
frequently of their own accord and in lively colors, gradually
return more rarely and in paler colors, and can be reproduced
by voluntary effort only with difficulty and in part. After a
longer period even this fails, except, to be sure, in rare instances.
Names, faces, bits of knowledge and experience that had seemed
lost for years suddenly appear before the mind, especially in
dreams, with every detail present and in great vividness; and
it is hard to see whence they came and how they managed to
keep hidden so well in the meantime. Psychologists — each in
accordance with his general standpoint — interpret these facts
from different points of view, which do not exclude each other
entirely but still do not quite harmonise. One set, it seems, lays
most importance on the remarkable recurrence of vivid images
even after long periods. They suppose that of the perceptions
caused by external impressions there remain pale images,
" traces," which, although in every respect weaker and more
flighty than the original perceptions, continue to exist unchanged
in the intensity possessed at present. These mental iniages can-
not compete with the much more intense and compact percep-
tions of real life; but where the latter are missing entirely or
partly, the former domineer all the more unrestrainedly. It is
also true that the earlier images are more and more overlaid,
so to speak, and covered by the later ones. Therefore, in the
case of the earlier images, the possibility of recurrence offers
itself more rarely and with greater difficulty. But if, by an
accidental and favorable grouping of circumstances, the accumu-
62
Retention and Obliviscence as a Function of the Time 63
lated layers are pushed to one side, then, of course, that which
was hidden beneath must appear, after whatever lapse of time,
| in its original and still existent vividness.1
For others2 the ideas, the persisting images, suffer changgs
which more and more affect thei? nature ; the concept of obscura-
tion comes in here. Older ideas are repressed and forced to sink 4
down, so to speak, by the more recent ones. As time passes one
of these general qualities, inner clearness and intensity of con-/
sciousness, suffers damage. Connections of ideas and series of j
ideas are subject to the same process of progressive weakening;
it is furthered by a resolution of the ideas into their components,
as a result of which the now but loosely connected members are
eventually united in new combinations. The complete disap-
pearance of the more and more repressed ideas occurs only j
after a long time. But one should not imagine the repressed
ideas in their time of obscuration to be pale images, but rather
to be tendencies, " dispositions," to recreate the image contents
forced to sink down. If these dispositions are somehow sup-
ported and strengthened, it may happen at any one moment that
1 This is the opinion of Aristotle and is still authoritative for many
people. Lately, for instance, Delboeuf has taken it up again, and has
used it as a complement to his " theorie generate de la sensibilite." In
his article, Le sommeil et les reves (Rev. Philos. IX, p. 153 f.), he says:
" Nous voyons maintenant que tout acte de sentiment, de pensee ou de
volition en vertu d'une loi universelle imprime en nous une trace plus
ou moins profonde, mais indelebile, generalement gravee sur une infinite
de traits anterieurs, surchargee plus tard d'une autre infinite de linea-
ments de toute nature, mais dont 1'ecriture est neanmoins indefiniment
susceptible de reparaitre vive et nette au jour." (We see now that by
a general law every act of feeling, thought or will leaves a more or less
deep but indelible impress upon our mind, that such a tracing is usually
graven upon an infinite number of previous traces and later is itself over-
laid with innumerable others but nevertheless is still capable of vivid
and clear reappearance.) It is true that he proceeds: "neanmoins . . .
il y a quelque verite dans 1'opinion qui veut que la memoire non seulement
se fatigue mais s'oblitere" (nevertheless . . . there is some truth
in the opinion that memory not only becomes fatigued but that it dis-
appears"), but he explains this by the theory that one memory might
hinder another from appearing. " Si un souvenir rre chasse pas I'autre
on peut du moins pretendre qu'un souvenir empeche 1'autre et qu'ainsi
pour la substance cerebrale, chez 1'individu, il y a un maximum de
saturation." (If one recollection does not actually drive out another,
it may at least be maintained that one recollection hinders the other and
that thus the brain of each individual is saturated.)
The curious theory of Bain and others that each idea is lodged in
a separate ganglion cell, an hypothesis impossible both psychologically
and physiologically, is also rooted to a certain extent in Aristotle's view.
"Herbart and his adherents. See, for instance, Waitz, Lehrbuch der
Psychologic Sect. 16.
64 Memory
the repressing and hindering ideas become depressed themselves,
and that the apparently forgotten idea arises again in perfect
clearness.
A third view holds that, at least in the case of complex ideas,
obliviscence consists in the crumbling into parts and the loss of
separate components instead of in general obscuration. The idea
of resolution into component parts recently spoken of supplies
here the only explanation. " The image of a complex object is
dim in our memory not because as a whole with all its parts
present and in ordei/it is illuminated by a feebler light of con-
sciousness, but it is because it has become incomplete. Some
parts of it are entirely lacking. Above all the precise connection
of those still extant is, in general, missing and is supplied only by
the thought that some sort of union once existed between them ;
the largeness of the sphere in which, without being able to
make a final decision, we think this or that connection equally
probable, determines the degree of dimness which we are to
ascribe to the idea in question."1
Each of these opinions receives a certain, but not exclusive,
support from the actual inner experiences, or experiences sup-
posed to be actual, which we at times have. And what is the
reason? It is that these fortuitous and easily obtained inner
experiences are much too vague, superficial and capable of various
interpretations to admit in their entirety of only a single inter-
pretation, or even to let it appear as of preponderating proba-
bility. Who could, with even tolerable exactness, describe in its
gradual course the supposed overlaying or sinking or crumbling
of ideas? Who can say anything satisfactory about the inhibi-
tions caused by series of ideas of different extent, or about the
disintegration that a firm complex of any kind suffers by the
use of its components in new connections? Everybody has his
private " explanation " of these processes, but the actual condi-
/tions which are to be explained are, after all, equally unknown
ifio all of us.
If one considers the limitation to direct, unaided observation
and to the chance occurrence of useful experiences, there seems
but little prospect or improvement in conditions. How will
one for example determine the degree of obscuration reached
at a certain point, or the number of fragments remaining? Or
'Lotze, Metaphysik (1870), p. 521; also Mikrokosmos (3) I, p. 231 ff.
Retention and Obliviscence as a Function of the Time 65
how can the probable course of inner processes be traced if
the almost entirely forgotten ideas return no more to con-
sciousness ?
Section 27. Methods of Investigation of Actual Conditions
By the help of our method we have a possibility of indirectly
approaching the problem just stated in a small and definitely
limited sphere, and, by means of keeping aloof for a while from
any theory, perhaps of constructing one.
After a definite time, the hidden but yet existent dispositions
laid down by the learning of a syllable-series may be strengthened
by a further memorisation of the series, and thereby the remain-
ing fragments may be united again to a whole. The work neces-
sary for this compared with that necessary when such disposi-
tions and fragments are absent gives a measure for what has
been lost as well as for what remains. The inhibitions which
idea-groups of different sorts or extents may occasion in rela-
tion to others must, as a result of the interposition of well defined
complexes of ideas between learning and relearning, betray itself |
in the more or less increased work of relearning. The loosening \
of a bond of connection by some other use of its components
can be investigated in a similar manner as follows : after a certain
series has been studied, new combinations of the same series
are memorised and the change in the amount of work necessary
for relearning the original combination is then ascertained.
First, I investigated the first mentioned of these relations and
put the question : If syllable series of a definite kind are learned
by heart and then left to themselves, how will the process of
forgetting go on when left merely to the influence ofjime or the .
daijyjsyents of life which fill it? The determination of the losses
suffered was made in the way described : after certain intervals
of time, the series memorised were relearned, and the times
necessary in both cases were compared.
The investigations in question fell in the year 1879-80 and
comprised 163 double tests. Each double test consisted in learn- ^
ing eight series of 13 syllables each (with the exception of 38
double tests taken from 11-12 A. M. which contained only six
ceries each) and then in relearning them after a definite time.
The learning was continued untif twd errorless recitations of the
series in question were possible.^The relearning was carried
to the same point; it occurred at one of the following seven
66 Memory
times, — namely, after about one third of an hour, after i hour,
after 9 hours, one day, two days, six days, or 31 days.
The times were measured from the completion of the first
set of first learnings, as a consequence of which no great accuracy
was required in case of the longer intervals. The influence of
the last four intervals was tested at three different times of
day (p. 33). Some preliminary remarks are necessary before
the results obtained can be communicated.
Similar experimental conditions may be taken for granted in
the case of the series relearned after a number of whole days.
At any rate there is no way of meeting the actual fluctuations
even when external conditions are as far as possible similar, other
than by a multiplication of the tests. Where the inner dissimi-
larity was presumably the greatest, namely after the interval of
an entire month, I approximately doubled the number of tests.
In the case of an interval of nine hours and an interval of
one hour between learning and relearning, there existed, how-
\ ever, a noticeably constant difference in the experimental con- >
ditions. - In the later hours of the day mental vigor and receptivity;
are less. The series learned in the morning and then relearned
at a later hour, aside from other influences, require more work
for relearning than they would if the relearning were done at
a time of mental vigor equal to that of the original learning.
Therefore, in order to become comparable, the numerical values
found for relearning must suffer a diminution which, at least
in the case of the 8 hour interval, is so considerable that it
cannot be neglected. It must be ascertained how much longer
it takes to learn at the time of day, B, series which were learned
in " a " seconds at the time of day, A. The actual determina-
tion of this quantity presupposes more tests than I, up to the
present, possess. If a necessary but inexact correction is applied
to the numbers found for i and for 8 hours, these become even
more unreliable than if left to themselves.
In the case of the smallest interval, one third of an hour, the
same drawback reappears, though to a less degree; but it is
probably compensated for by another circumstance. The interval
as a whole is so short that the relearning of the first series of
a test followed almost immediately or after an interval of one
or two minutes upon the learning of the last series of the same
test. For this reason the whole formed, so to speak, one con-
Retention and Obliviscence as a Function of the Time 67
tinuous test in which the relearning of the series took place
under increasingly unfavorable conditions as regards mental
freshness. But on the other hand the relearning after such a S
short interval was done rather quickly. It took hardly half of
the time required for the learning. By this means the interval
between the learning and relearning of a certain series became
gradually smaller. The later series therefore had more favor-
able conditions with regard to the time interval. In view of
the difficulty of more accurate determinations, I have taken it
for granted that these two supposed counteracting influences
approximately compensated each other.
Section 28. Results
In the following table I denote by:
L the time of first learning of the series in seconds, just as they
were found, therefore including the time for the two reci-
tations.
WL the time for relearning the series also including the recita-
tions.
WLk the time of relearning reduced where necessary by a cor-
rection.
J the difference L — WL or L — WLk, as the case may be — that
is, the saving of work in the case of relearning.
Q the relation of this saving of work to the time necessary for
the first learning, given as a per. cent. In the calculation
of this quotient I considered only the actual learning time,
the time for recitation having been subtracted.1
The latter was estimated as being 85; seconds for two recita-
tions of 8 series of 13 syllables each ; that would correspond to
*A theoretically correct determination of the Probable Errors of
the differences and quotients found would be very difficult and trouble-
some. The directly observed values L and WL would have to be made
the basis of it. But the ordinary rules of the theory of errors cannot
be applied to these values, because these rules are valid only for obser-
vations gained independently of one another, whereas L and WL are
inwardly connected because they were obtained from the same series.
The source of error, " difficulty of the series," does not vary by chance,
but in the same way for each pair of values. Therefore I took here
the learning and relearning of the series as a single test and the
resulting A or Q, as the case may be, as its numerical representative.
From the independently calculated A and Q, the probable errors were
then calculated just as from directly observed values. That is sufficient
for an approximate estimate of the reliability of the numbers.
68
Memory
a duration of 0.41 seconds for each syllable (p. 31).
Thus Q = loo A
L— 85
Finally A, B, C mean the previously mentioned times of day,
10-11 A. M., 11-12 A. M., 6-8 P. M.
I. 19 minutes. 12 tests. Learning and relearning at the time A.
L
WL
A
Q
1156
467
689
64.3
1089
528
561
55.9
1022
492
530
56.6
1146
483
663
62.5
1115.
490
625
60.7
1066
447
619
63.1
985
453
532
59.1
1066
517
549
56.0
1364
540
824
64.4
975
577
398
44.7
1039
528
511
53.6
952
452
500
57.7
m=1081
498
583
58.2
P.E.m=l
II. 63 minutes. 16 tests. The learning at the time A, the relearning
at the time B. For ascertaining the influence of this difference in the time
of day I have the following data. Six series qf 13 syllables each were learned
at the time B (not including the timeof recitation) in 807seconds (P.E.m=10)
as an average of 39 tests. Just as many series of the same kind were learned
at the time A in 763 seconds (P.E.m=7) as an average of 92 tests. Thus the
values found in the later period are about 5 per cent, of their own amount
too large as compared with those obtained irf'the earlier period. Therefore
the times found for relearning at the time B must be decreased by about
5 per cent, to make them comparable with those of learning.
L
WL
WLk
A
Q
1095
625
594
501
49.6
1195
821
780
415
37.4
1133
669
636
497
47.4
1153
687
653
500
46.8
1134
626
595
539
51.4
1075
620
589
486
49.1
1138
704
669
469
44.5
1078
565
537
541
54.5
1205
770
731
474
42.3
1104
723
687
417
40.9
886
644
612
274
34.2
958
591
562
396
45.4
1046
739
702
344
35.8
1122
790
750
372
35.9
1100
609
579
521
51.3
1269
709
674
595
50.0
m 1106
681
647
459
44.2
Retention and Obliviscence as a Function of the Time 69
III. 525 minutes. 12 tests. The learning at the time A, the relearnine
at the time C. The different influence of the two times of day is calculated
as follows: eight series of 13 syllables each required, with 38 tests at time
C, 1173 seconds (P.E.m— 10); similar series with 92 tests at time A required
1027 seconds (P.E.m=8). The first number is approximately 12 per cent,
of its own value larger than the second; therefore I have subtracted that
much from the numerical values found for the time C.
L
WL
WLk
A
Q
1219
921
811
408
36.0
975
815
717
258
29.0
1015
858
755
260
28.0
954
784
690
264
30.4
1340
955
840
500
39.8
1061
811
714
347
35.6
1252
784
690
562
48.2
1067
860
757
310
31.6
1343
1019
897
446
35.5
1181
842
741
440
40.1
1080
799
703
377
37.9
1091
806
709
382
38.0
m 1132
855
752
380
35.8
P.E.m=l
IV. One day. 26 tests, of which 10 were at time A, 8 at time B (here as
everywhere consisting of only 6 series each), 8 at time C.
L
WL
J
Q
1072
811
261
26.4
1369
861
508
39.6
1227
823
404
35.4
1263
793
470
39.9
1113
754
359
34.9
1000
644
356
38.9
1103
628
475
46.7
888
754
134
16.7
1030
829
201
21.3
1021
660
361
38.6
m 1109
756
353
33.8
P.E.m==2
7o
Memory
B
L
WL
A
Q
889
824
897
825
854
863
742
907
650
537
593
599
562
761
433
653
239
287
304
226
292
122
309
254
29.0
37.8
36.5
29.7
37.0
14.9
45.6
30.1
m 853
599
254
32.6
P.E.m=2.2
L
WL
A
Q
1212
1215
1096
1191
1256
1295
1146
1064
935
797
647
684
898
781
936
750
277
418
449
507
358
514
210
314
24.6
37.0
44.4
45.8
30.6
42.6
19.8
32.1
TO 1184
803
381
34.6
P.E.m=2.3
Retention and Obliviscence as a Function of the Time 7 1
The average differences between times of learning and relearning at the
different times of day vary somewhat with regard to their absolute values.
(Of course in the case of B the number 254 must, first be multiplied by 4/3,
because it is derived from only 6 series.) But the relations of these differ-
ences to the times of first learning (the Q's) harmonize sufficiently well.
If, therefore, all theQ's are combined in a general average, Q=33.7 (P.E.m=1.2).
V. Two days. 26 tests; 11 of these at the time A, 7 at B, 8 at C.
A
L
WL
A
Q
1066
895
171
17.4
1314
912
402
32.7
963
855
108
12.3
964
710
254
28.9
1242
888
354
30.6
1243
710
533
46.0
1144
895
249
23.5
1143
874
269
25.4
1149
953
196
18.4
1090
855
235
23.4
1376
847
529
41.0
m 1154
854
300
27.2
P.E.m=2.3
B
L
WL
A
. Q
752
1087
1073
826
905
811
782
549
740
620
693
548
763
618
203
347
453
133
357
48
164
29.5
33.9
44.9
17.5
42.4
6.4
22.8
m 891
647
244
28.2
P.E.m=3.5
Memory
C
L
WL
A
Q
1246
1231
1273
1319
1125
1275
1322
1170
889
885
1039
925
971
891
857
880
357
346
234
394
154
384
465
290
31.6
30.2
19.7
31.9
14.8
32.3
37.6
26.7
m 1245
917
328
28.1
P.E.m=1.8
The combination of the three average values of Q, which are stated ia
per cents and lie close to each other,forthe 26 tests gives Q=27.8 (P.E.m=1.4)
VI. Six days. 26 tests, 10 at the time A, 8 at B, 8 at C.
A
L
WL
A
Q
1076
868
208
21.0
992
710
282
31.1
1082
756
326
32.7
1260
973
287
24.4
1032
864
168
17.7
1010
955
55
5.9
1197
818
379
34.1
1199
828
371
33.3
943
697
246
28.7
1105
868
237
23.2
m 1090
834
260
25.2
P.E.m=1.9
Retention and Obliviscence as a Function of the Time
B
73
L
WL
A
- Q
902
793
848
871
1034
745
975
805
564
517
639
709
649
728
645
766
338
276
209
162
385
17
330
39
40.3
37.9
26.5
20.1
39.7
2.5
36.2
5.3
m 872
652
220
26.1
P.E.m=4
L
WL
J
Q
1246
1334
1293
1401
1214
1299
1358
1305
922
1097
939
988
992
1045
1047
881
324
237
354
413
222
254
311
424
27.9
19.0
21.0
31.4
19.7
20.9
24.4
34.8
m 1306
989
317
24.9
P.E.m=1.6
74
Memory
The average of the total 26 savings of work, stated in per cents, is 25.4
(P.E.m=1.3).
VII. 31 days. 45 tests; 20 at the time A, 15 at B, 10 at C.
A
L
WL
A
Q
1069
813
256
26.0
1109
785
324
31.6
1268
858
410
34.7
1280
902
378
31.6
1180
848
332
30.3
1095
888
207
20.5
1089
988
101
10.1
1113
1043
70
6.8
1090
1025
65
6.5
997
876
121
13.3
1116
934
182
17.7
1060
893
167
17.1
930
796
134
15.9
1030
769
261
27.6
980
862
118
13.2
1079
805
274
27.6
1254
978
276
23.6
1164
938
226
20.9
1127
869
258
24.8
1268
972
296
25.0
m 1115
892
223
21.2
P.E.m=1.3
B
L
WL
A
Q
831
638
193
25.2
867
516
351
43.7
960
748
212
23.7
828
675
153
20.0
859
705
154
19.4
838
661
177
22.9
946
887
59
6.7
833
780
53
6.9
696
532
164
25.9
757
626
131
18.9
906
733
173
20.5
1024
915
109
11.4
930
780
150
17.3
899
756
143
17.1
1018
705
313
32.8
m 879
710
169
20.8
P.E.m=1.4
Retention and Obliviscence as a Function of the Time 7 5
C
L
WL
A
Q
1424
1004
420
31.4
1307
1102
205
16.4
1351
893
458
36.2
1245
1090
155
13.4
1258
895
363
31.0
1155
1070
85
7.9
1219
800
419
36.9
1278
1110
168
14.1
1120
1051
69
6.7
1250
1055
195
16.7
m 1261
1007
254
21.1
P.E.m=2.7
The average of 45 savings of work expressed in per cents— 21.1 (P.E.m=0.8).
A hasty glance at the figures above reveals the fact that for
each interval of time the savings in work which become evident
when the series is relearned have very fluctuating values. (This
saving in work is each time the measure for the amount re-
membered at the end of the interval.) This is especially the
case with their absolute values (A), but is also the case with
the relative values (Q). The results are taken from the earlier
period and suffer from several disturbing influences to which
my attention was first drawn by the tests themselves.
In spite of all irregularities in detail, however, they group
themselves as a whole with satisfactory certainty into an har-
monious picture. As a proof of this the absolute amount of
the saving in work is of less value. The latter evidently depends
upon the time of day — i.e., upon the changes in the time of the
first learning dependent upon it. When this change is greatest
(time C), A also is greatest; for the time B, they are in ft of
the cases larger than for the time A (after multiplying by 4/3).
On the other hand, the values (Q) found for the relation of each
saving of work to the time originally spent, are apparently almost
independent of this ratio. Their averages are close together for
all three times of day, and do not show any character of increase
or decrease in the later hours. Accordingly I here tabulate the
latter.
76
Memory
I
II
III
IV
So much of the series
learned was retained that
The amount forgotten
No.
After X
hours
in relearning a saving of
Q % of the time of original
learning was made
P.E.m
was thus equivalent to
v % of the original in
terms of time of learning
X=
Q=
v=
1
0.33
58.2
1
41.8
2
1.
44.2
1
55.8
3
8.8
35.8
1
64.2
4
24.
33.7'
1.2
66.31
5
48.
27.8
1.4
72.21
6
6x24
25.4
1.3
74.6
7
31x24
21.1
0.8
78.9
Section 29. Discussion of Results
1. It will probably be claimed that the fact that forgetting
would be very rapid at the beginning of the process and very
slow at the end should have been foreseen. However, it would
be just as reasonable to be surprised at this initial rapidity and
later slowness as they come to light here under the definite con-
ditions of our experiment for a certain individual, and for a
series of 13 syllables. One hour after the end of the learning,
the forgetting had already progressed so far that one half the
amount of the original work had to be expended before the
series could be reproduced again ; after 8 hours the work to be
made up amounted to two thirds of the first effort. Gradually,
however, the process became slower so that even for rather long
periods the additional loss could be ascertained only with diffi-
culty. After 24 hours about one third was always remembered ;
after 6 days about one fourth, and after a whole month fully
one fifth of the first work persisted in effect. The decrease of
this after-effect in the latter intervals of time is evidently so
slow that it is easy to predict that a complete vanishing of the
effect of the first memorisation of these series would, if they
had been left to themselves, have occurred only after an indefin-
itely long period of time.
2. Least satisfactory in the results is the difference between
the third and fourth values, especially when taken in connection
with the greater difference between the fourth and fifth numbers.
In the period 9-24 hours the decrease of the after-effect would
Retention and Obliviscence as a Function of tlie Time 7 7
accordingly have been 2^ per cent. In the period 24 to 48 hours
it would have been 6.1 per cent; in the later 24 hours, then, about
three times as much as in the earlier 15. Such a condition is
not credible, since in the case of all the other numbers the
decrease in the after-effect is greatly retarded by an increase in !
time. It does not become credible even under the plausible ;
assumption that night and sleep, which form a greater part of
the 15 hours but a smaller part of the 24, retard considerably
the decrease in the after-effect.
Therefore it must be assumed that one of these three values is - i
greatly affected by accidental influences. It would fit in well
with the other observations to consider the number 33.7 per cent
for the relearning after 24 hours as somewhat too large and to
suppose that with a more accurate repetition of the tests it would
be i to 2 units smaller. However, it is upheld by observations
to be stated presently, so that I am in doubt about it.
3. Considering the special, individual, and uncertain character
of our numerical results no one will desire at once to know
what " law " is revealed in them. However, it is noteworthy
that all the seven values which cover intervals of one third of
an hour in length to 31 days in length (thus from singlefold to
2,ooofold) may with tolerable approximation be put into a rather
simple mathematical formula. I call:
t the time in minutes counting from one minute before the
_end of the learning,
~~ FtKe saving of work evident in relearning, the equivalent of
the amount remembered from the first learning expressed in per-
centage of the time necessary for this first learning,
c and k two constants to be defined presently
Then the following formula may be written:
100 k
By using common logarithms and with merely approximate
estimates, not involving exact calculation by the method of least
squares,
£=1.84
7 8 Memory
Then the results are as follows:
t
6
Observed
b
Calculated
A
20
58.2
57.0
+ 1.2
64
44.2
46.7
— 2.5
526
35.8
34.5
+ 1.3
1440
33.7
30.4
+ 3.3
2 x 1440
27.8
28.1
- 0.3
6 x 1440
25:4
24.9
+ 0.5
31 x 1440
21.1
21.2
— 0.1
I
The deviations of the calculated values from the observed
values surpass the probable limits of error only at the second
and fourth values. With regard to the latter I have already
expressed the conjecture that the test might have given here too
large a value ; the second suffers from an uncertainty concerning
the correction made. By the determination made for t, the
formula has the advantage that it is valid for the moment in
which the learning ceases and that it gives correctly b =? 100.
In the moment when the series can just be recited, the relearning,
of course, requires no time, so that the saving is equal to the
work expended.
Solving the formula for k we have
k = -
100 — b
This expression, 100 — b the complement of the work saved, is
nothing other than the work required for relearning, the equiva-
lent of the amount forgotten from the first learning. Calling this,
v, the following simple relation results :
b k
v (log/)0
To express it in words: when nonsense series of 13 syllables
each were memorised and relearned after different intervals, the
quotients of the work saved and the work required were about
inversely proportional to a small power of the logarithm of those
intervals of time. To express it more briefly and less accurately :
the quotients of the amounts retained and the amounts forgotten
were inversely as the logarithms of the times.
Retention and Obliviscence as a Function of the Time 79
Of course this statement and the formula upon which it rests
have here no other value than that of a shorthand statement of
the above results which have been found but once and under
the circumstances described. Whether they possess a more gen-
eral significance so that , under other circumstances or with other
individuals, they might find expression in other constants I can-
not at the present time say.
Section jo. Control Tests
At any rate, even though only for my own case, I can to a
certain extent give support to two of the values mentioned by
tests which were made at other periods.
From a period even further back than that of the investigations
above mentioned I possess several tests with series of ten syllables,
fifteen series composing one test. The series were first memorised
and then, at an average of 18 minutes after the first learning,
each series was relearned. Six tests had the following results : —
L
LW
A
Q*
848
436
412
57.5
963
535
428
50.9
921
454
467
58.5
879
444
435
57.5
912
443
469
59.4
821
461
360
51.6
m = 891
462
429
56.0
* The time subtracted from the L when calculating the Q for two repro-
ductions of 15 series is 123 seconds.
When relearning series of ten syllables each, 18 minutes after
the first memorisation, 56 per cent of the work originally ex-
pended was therefore saved. The number agrees satisfactorily
with the one found above (p. 68) for the relearning of
series of syllables of 13 syllables each after 19 minutes, 58 per
cent. Also the fact that the latter, notwithstanding the longer
interval, is still a little greater, harmonises completely, as will
be seen, with the results of the next chapter. According to them,
shorter series, when memorised, are forgotten a little more quickly
than longer ones.
8o
Memory
From the period of 1883-84, I have seven tests, consisting of
nine series of 12 syllables each that were relearned 24 hours after
the first memorisation. The following results were obtained :
L
LW
A
Q
791
750
911
725
783
879
689
508
522
533
494
593
585
535
283
228
378
231
190
294
154
37.9
32.3
43.6
33.9
27.1
35.2
23.9
m 790
539
251
33.4
P.E.m=1.7
The after-effect _of,the first memorisation still noticeable after
24 hours, was here equivalent to a saving ofjwork of 33.4 per cent
of the first expenditure. This number also agrees satisfactorily
with the one communicated above for the relearning of series
of 13 syllables each after 24 hours (33.7 per cent), although
these two were obtained at far separated time-periods and in the
course of widely different investigations.
CHAPTER VIII
RETENTION AS A FUNCTION OF REPEATED
LEARNING
Section 31. Statement of the Problem and the Investigation
Series of syllables which have been learned by heart, forgotten,
and learned anew must be similar as to their inner conditions
at the times when they can be recited. The energy of the idea-
tional activity which is directed upon them and which serves to
establish them is in both cases so far heightened that quite similar
combinations of movements occur in connection with them. For -f-
the period after the recital this inner similarity ceases. The series
are gradually forgotten, but — as is sufficiently well known — the
series which have been learned twice fade away much more
slowlyxthan those which have been learned but once. If the re-
learning is performed a second, a third or a greater number of
times, the series are more deeply engraved and fade out less
easily and finally, as one would anticipate, they become pos-
sessions of the soul as constantly available as other image-series
which may be meaningful and useful.
I have attempted to obtain numerical data on the relation of
dependence which exists between the permanence of retention
of a series and the number of times it has been brought, by
means of renewed learning, to a just possible reproduction. The
relation is quite similar to that described in Chapter VI as exist-
ing between the surety of the series and the number of its repe-
titions. In the present case, however, the repetitions do not take
place all at once, but at separate times and in ever decreasing
frequency. On account of our limited insight into the inner
connection of these processes we would not be justified in ventur-
ing an assertion about one relation on the basis of the other.
Only one value of the time interval between the separate re-
learnings was chosen, namely, 24 hours. Instead of changing
intervals, series of different lengths were chosen for the investi-
ff
82
Memory
gation, the lengths being 12, 24 and 36 syllables. A single test
consisted of nine series of the first length, or three of the second,
or two of the third. In addition to this I carried out several
tests with six stanzas of Byron's " Don Juan."
The plan of the experiment was, then, as follows : The required
number of series was first learned and then, at the same hour
on successive days, it was relearned to the point of first possible
reproduction. In the case of the series of syllables, the number
of days was six ; in the case of Byron's stanzas, it was only four.
Thus, on the fifth day, the stanzas were correctly repeated
without any preliminary reproduction and the problem, accord-
ingly, no longer existed. For each kind of series, seven trials
were employed. The total number of separate tests was, in con-
sequence, 154, a number of which required only a few minutes
for their execution.
The entries of the following tables indicate the repetitions
which were necessary in order to bring the series concerned to
the first possible reproduction (including this) ; the Roman fig-
ures designate the successive days.
1. Nine series of 12 syllables each.
I
II
III
IV
V
VI
158
151
175
149
163
173
138
102
107
105
102
124
117
106
71
74
84
72
69
86
71
50
42
60
54
61
64
59
38
34
36
35
35
42
37
30
30
33
28
31
37
30
m 158
P.E.m 3.4
109
2
75
1.7
56
2
37
0.7
31
0.7
2. Three series of 24 syllables each.
I
II
III
IV
V
VI
122
127
154
139
133
142
124
73
73
78
61
73
66
70
45
40
47
33
36
42
36
29
25
27
17
26
26
24
21
18
18
12
18
17
16
16
15
12
10
14
14
14
m 134
P.E.m 2.9
71
1.4
40
1.3
25
1
17
0.7
14
0.5
Retention as a Function of Repeated Learning
3. Two series of 36 syllables each.
I
II
III
IV
V
VI
115
124
137
109
87
105
110
52
59
55
48
39
40
41
23
33
26
21
21
22
21
18
21
17
16
15
17
16
9
12
12
10
13
12
10
8
10
8
10
8
10
11
m 112
P.E.m 4
48
2
24
1.1
17
0.5
11
0.4
9
0.3
4. Six stanzas of Byron's "Don Juan" (Canto X).
I
II
III
IV
53
56
53
49
53
53
50
29
29
30
25
27
34
28
18
16
15
14
16
21
17
11
10
10
9
10
9
10
m 52
P.E.mO.6
29
0.7
17
0.6
10
0.2
In order to bring out more clearly the separate relations which
exist between the resulting averages, it is necessary to reduce
the total figures to the same unit — i.e., to divide them in each case
by the number of series constituting a single trial. If this is
done and the repetition necessary for the recital is deducted, the
following table results, fractions being given to the nearest half
or quarter.
Number of
syllables in
Number of repetitions which, on the average, were
necessary for the bare learning of the series on suc-
cessive days
one series
I
II
III
IV
V
VI
12
16.5
11.
7.5
5.
3.
2.5
24
44.
22.5
12.5
7.5
4.5
3.5
36
55.
23.
11.
7.5
4.5
3.5
1 stanza D. J.
7.75
3.75
1.75
0.5
(0).
(0).
From several points of view these numbers require further
consideration.
, 4
Memory
Section 32. Influence of the Length of the Series
If the results for the first and second days are examined, wel-
come, though not surprising, supplementary data on the relation
of dependence presented in Chapter V is obtained. In the
former chapter, it was shown that, as the length of the series
increased, the number of repetitions requisite increased very
rapidly. Here, the result is that the effect of this need of more
numerous repetitions in the cases investigated consists not merely
in making the series just reproducible, but also in the firmer
establishment of the longer series. After an interval of 24 hours
they could be relearned to the point of being just reproducible
with a saving both absolutely and relatively greater than with the
shorter series.
The following table makes this relation clear.
Number of
syllables in
one series
Number of
repetitions
for learning
Saving in repeti-
tions in relearning
after 24 hours
Saving in % of
requirement for
first learning
12
24
36
16.5
44
55
5.5
21.5
32
33.3
48.9
58.2
The saving in the case of the shortest of the series investigated
is one third for the second learning as compared with the first ;
while with the longest series, it is six tenths. It can be said,
therefore, that by being learned to the first possible .reproduction
the series of 36 syllables is approximately twice as firmly estab-
lished as the series of 12 syllables.
In this there is nothing new. On the basis of the familiar
experience that that which is learned with difficulty is better
retained, it would have been safe to prophesy such an effect
from the greater number of repetitions. That which probably
would not have been anticipated and which also demands atten-
tion, is the more definite determination of this general relation.
So far as the numbers go, they seem to show that, between the
increase of the repetitions necessary for the first learning and
the inner stability of the series effected by them, there is no
proportionality. Neither the absolute nor the relative saving of
work advances in the same way as the number of repetitions;
Retention as a Function of Repeated Learning 85
•—>
the former advance much faster and the latter noticeably more j
slowly. It cannot, therefore, be said in any exact sense of the;
words that the more frequently a series needs to be repeatedi
to-day in order to be learned by heart the more repetitions will
be saved in its reproduction after 24 hours. The relation in
force seems to be much more complicated and its exact deter-
mination would require more extensive investigations.
The relation of repetitions for learning and for repeating
English stanzas needs no amplification. These were learned by
heart on the first day with less than half of the repetitions neces-
sary for the shortest of the syllable series. They acquired ,
thereby so great stability that for their reproduction on the next
day proportionally no more work was needed than for the series
of 24 syllables — i.e., about half of the first expenditure.
Section 33. Influence of Repeated Learning
We will now take into consideration the results for the suc-
cessive days taken as a whole. On each day the average number
of repetitions necessary for the committing of a given series
is less than on the preceding day. With the longer series, in
whose case the first output of energy is great, the decrease in j
the amount of work each time necessary to reach the first pos- j
sible reproduction is proportionally rapid. With the shorter
series, where the first output is small, the decrease is propoM
tionally slow. On this account the numbers of repetitions neces-
sary for the different series approach each other more and more.
With the series of 24 and 36 syllables this is apparent even from
the second day ; from the fourth day on, the numbers ^all abso-
lutely together. And by the fifth day they have approached very
closely to the number of repetitions still necessary, in accordance '/
with the slower decrease, for the learning of the 12-syllable
series.
A simple conformity to law cannot be discovered in this
successively decreasing necessity for work. The quotients of
the necessary repetitions on two successive days approach unity.
If the final repetition were not subtracted, as was done in the
concluding table of Section 31, but were reckoned in, this ap-
proach would be somewhat faster. (In the case of the English
stanzas it generally takes place only under these conditions.)
86
Memory
Nevertheless the course of the numbers cannot be described by
a simple formula.
Rather is this the case if one takes into consideration, not
the gradually decreasing necessity for work, but the just as
gradually decreasing saving of work.
Number of repetitions saved on learning a series on
Number of
the following day; average values
No.
syllables
in one series
I-II
II-III
III-IV
IV-V
V-VI
1
12
5.5
3.5
2.5
2
0.5
2
24
21.5
10.0
5.0
3
1.0
3
36
32.0
12.0
3.5
3
1.0
4
1 stanza D. J.
4.0
2.0
1.25
0.5
Of these numerical sequences two — namely, the second and
fourth rows — form with great approximation a decreasing
geometrical progression with the exponent 0.5. Very slight
changes in the numbers would be sufficient fully to bring out
this conformity. By slight changes, the first row might also
be transformed into a geometrical progression with the exponent
0.6. On the contrary, a large error in the results of investiga-
tion would need to be assumed in order to get out of Row 3
any such geometric progression (whose exponent would then be
about one third).
If not for all, yet for most, of the results found, the rela-
tion can be formulated as follows: If series ,of nonsense
syllables or verses of a poem are on several successive days
each time learned by heart to the point of the first possible
reproduction, the successive differences in the repetitions neces-
\ sary for this form approximately a decreasing geometrical pro-
• gression. In the case of syllable-series of different lengths, the
exponents of these progressions were smaller for the longer
series and larger for the shorter ones.
Although the tests just described were individually not more
protracted than the others, yet relatively they required many
days, and the average values were consequently derived from
a rather small number of observations. So here, even more
than elsewhere, I am unable to affirm that the simple conformity
to law approximately realised in the results so far obtained would
Retention as a Function of Repeated Learning 87
stand the test of repetition or wider extension of research. I
content myself by calling attention to it without emphasis.
Section 34. Influence of the Separate Repetitions
The problem of the present chapter is, as has already been
pointed out, closely related to that of Chapter VI. In both
cases the investigation, concerns the influence of an increasing
number of repetitions on the fixation of the series of syllables, ;
a fixation made increasingly stronger thereby. In the former
case the total number of repetitions immediately succeeded each\
other without regard to whether the spontaneous reproduction of j ' '
the series was obtained through them or to how it was obtained. V
In this case the repetitions were distributed over several days and L
the attainment of the first possible reproduction was employed
for their apportionment on the separate days. If, now, the
results obtained in both cases have, at least for my own per-
sonality, any wider validity, we should expect that in so far
as they are comparable, they would harmonise. That is, we
should expect in this case as in the former that the effect of
the later repetitions (therefore, those of the 2nd, 3rd, and later
days), would at first be approximately as great as that of the
earlier, and later would decrease more and more.
A more exact comparison is in the nature of the case not now
possible. In the first place, the series of Chapter VI and the
present ones are of different length. In the second place, the
detailed ascertainment of the effect of the repetitions of the
succssive days taken solely by themselves would be possible only
through assumptions which might be plausible enough on the
basis of the data presented, but which would be easily contro-
vertible on account of the insecurity of these data.
We found, for example, that nine 12-sy liable series were
learned on six successive days by means of 158, 109, 75, 56, 37
and 31 repetitions. The effect of the first 158 repetitions is
here immediately given in the 109 repetitions of the succeeding
day in the difference, 158 — 109. But if we wish to know the
intrinsic effect of these 109 repetitions, namely the saving
effected by them, on the third day, we could not simply take
the difference, 109 — 75. We should need to know, rather, with
how many repetitions (x) the series would have been learned
Memory
on the third day if no repetitions had occurred on the second,
and we should then have in the difference, x — 75, the separate
effect of the 109 repetitions actually given. Since the forgetting
increased somewhat from the second to the third day, x would
be somewhat greater than 109. In the same way, for the deter-
mination of the effect of the 75 repetitions of the third day,
we should need to learn in some way or other with how many
repetitions (y), the series would have been learned by heart on
the fourth day which, on the first day, required 158; and on
the second, 109. The difference, y — 56, would then give the
measure of that effect; and so on. For the ascertainment of
x, the results of Chapter VII give a certain basis. There the
result was that, in the case of 13-syllable series, the amount
forgotten at the end of 24 hours was to that forgotten at the
end of 2 x 24 hours as 66 to 72. But the employment of this
relation, itself insecure, «WoUW be justifiable only in case of the
i2-syllable series, and would accordingly not help in the deter-
mination of y, etc. One could at the best suppose that the
resulting quotients would approximate yet more closely to unity.
Accordingly I renounce these uncertain assumptions, and con-
tent myself with presenting the relations of the successive repe-
titions to the successive savings by showing that the presupposed
pure effect of the separate repetitions would be represented by
somewhat greater and presumably less divergent numbers.
Number of
syllable's of
each series
The following savings after 24 hours resulted from each
repetition on the separate days (in fractions of their
own value)
I
II
HI
IV
V
12
24
36
0.31
0.47
0.57
0.31
0.44
0.50
0.25
0.38
0.29
0.34
0.32
0.35
0.16
0.16
0.18
Although the course of these figures, which are, as has been
said, inexact as to their absolute values, is tolerably regular in
the case of the 24-syllable series only, its general character agrees
very well with what would be expected from the results of
Chapter IV. The effect of the repetitions is at first approxi-
Retention as a Function of Repeated Learning 89
mately constant, the saving in work which results from these
repetitions increases accordingly for a while proportional to
their number. Gradually the effect becomes less; and finally,
when the series has become so firmly fixed that it can be repeated
almost spontaneously after 24 hours, the effect is shown to be
decidedly less. The results of the fourth and the present chap-
ter, as far as can be seen, support each other.
Nevertheless, there is a noteworthy distinction to which I call
attention. \Yc found above (p. 60) that six i2-syllable series,
which had been learned at a given time with an average of 410
repetitions, could be learned by heart at the end of 24 hours with,
on the average, 41 repetitions. For a single 12-syllable series,
accordingly, 68 immediately successive repetitions had the effect
of making possible an errorless recital on the following day after
7 repetitions. T In the present research with distribution of the
repetitions over several days the same effect appears on the
fourth day: 9 12-sy liable series were learned by heart with 56
repetitions. Each series, therefore, was learned with about 6
repetitions. But the number of repetitions which were neces-
sary for the production of this effect in the case of the nine
series amounted to only 158+109 + 75 = 342. For a single
series, therefore, the number was 38. For the relearning of a
1 2-sy liable series at a definite time, accordingly, 38 repetitions,
distributed in a certain way over the three preceding days, had
just as favorable an effect as 68 repetitions made on the day
just previous. Even if one makes very great concessions to the
uncertainty of numbers based on so few researches, the differ-
ence is large enough to be significant. It makes the assumption^
probable that with any considerable number of repetitions a suit-
able distribution of them over a space of time is decidedly more j
advantageous than the massing of them at a single time.
With this result, found here for only very limited conditions,
the method naturally employed in practice agrees. The school-
boy doesn't force himself to learn his vocabularies and rules alto-
gether at night, but knows that he must impress them again in
the morning. A teacher distributes his class lesson not indif-
ferently over the period at his disposal but reserves in advance
a part of it for one or more reviews.
T
CHAPTER IX
RETENTION AS A FUNCTION OF THE ORDER OF
SUCCESSION OF THE MEMBERS OF THE SERIES
"How odd are the connections
Of human thoughts which jostle in their flight."
Section 55. Association according to Temporal Sequence and its
Explanation
I shall now discuss a group of investigations made for the
purpose of finding out the conditions of association. The results
of these investigations are, it seems to me, theoretically of
especial interest.
The non-voluntary_jre-emergence of mental images out of the
darkness of memory into the light of ccJnsciousness takes place,
as has already been mentioned, not at random and accidentally,
but in certain regular forms in accordance with the so-called laws
of association. General knowledge concerning these laws is as
old as psychology itself, but on the other hand a more precise
formulation of them has remained — characteristically enough —
a matter of dispute up to the very present. Every new presen-
tation starts out with a reinterpretation of the contejnts of a few
lines from Aristotle, and according to the condition of our knowl-
edge it is necessary so to do.
Of these " Laws," now — if, in accordance with usage and it
is to be hoped in anticipation of the future, the use of so lofty
a term is permitted in connection with formulae of so vague a
character — of these laws, I say, there is one which has never
been disputed or doubted. It is usually formulated as follows :
Ideas which have been developed simultaneously or in immediate
succession in the same mind mutually reproduce each_ other, and
do this with greater ease in the direction of the original suc-
cession and with a certainty proportional to the frequency with
which they were together.
90
Retention as a Function of Order of Succession 9 1
This form of non-voluntary reproduction is one of the best
verified and most abundantly established facts in the whole realm
of mental events. It permeates inseparably every form of repro-
duction, even the so-called voluntary form. The function of the
conscious will, for example, in all the numerous reproductions
oT^the syllable-series which we have come to know, is limited
to the general purpose of reproduction and to laying hold of the 1L
first member of the series. The remaining members follow auto-
mafjcally, so to speak, and thereby fulfill the law that things
which have occurred together in a given series are reproduced
in the same order.
However, the mere recognition of these evident facts has
naturally not been satisfying and the attempt has been made
to penetrate into the inner mechanism of which they are the
result. If for a moment we try to follow up this speculation
concerning the Why, before we have gone more than two steps
we are lost in obscurities and bump up against the limits of our
knowledge of the How.
It is customary to appeal for the explanation of this form of
association to the nature of the soul. Mental events, it is said,
are not passive happenings but the acts of a subject. What is
more natural than that this unitary being should bind together
in a definite way the contents of his acts, themselves also unified ?
Whatever is experienced simultaneously or in immediate suc-
cession is conceived in one act of consciousness and by that
very means its elements are united and the union is naturally
stronger in proportion to the number of times they are entwined
by this bond of conscious unity. Whenever, now, by any chance
one part only of such a related complex is revived, what else
can it do than to attract to itself the remaining parts ?
But this conception does not explain as much as it was intended
to do. For the remaining parts of the complex are not merely
drawn forth but they respond to the pull in an altogether definite
direction. If the partial contents are united simply by the fact
of their membership in a single conscious act and accordingly
all in a similar fashion, how does it come about that a sequence
of partial contents returns in precisely the same order and not
in any chance combination? In order to make this intelligible,
one can proceed in two ways.
\
\1
If
92 Memory
In the first place it can be said that the connection of the
things present simultaneously in a single conscious act is made
from each member to its immediate successor but not to mem-
bers further distant. This connection is in some way inhibited
I by the presence of intermediate members, but not by the inter-
position of pauses, provided that the beginning and end of the
pause can be grasped in one act of consciousness. Thereby return
is made to the facts, but the advantage which the whole plausible
appeal to the unitary act of consciousness offered is silently
abandoned. For, however much contention there may be over
the number of ideas which a single conscious act may compre-
hend, it is quite certain that, if not always, at least in most
cases, we include more than two members of a series in any one
conscious act. If use is made of one feature of the explanation,
the characteristic ol..uj}itji, as a welcome factor, the other side,
the manifoldness of the members, must be reckoned with, and
the right of representation must not be denied it on assumed
but unstatable grounds. Otherwise, we have only said, — and
it is possible that we will have to be content with that — that it
is so because there are reasons for its being so.
There is, consequently, the temptation to use this second form
of statement. The ideas which are conceived in one act of con-
sciousness are^jt is true,~ajl bound together, but notltTtrrg^ame
way. The strength of the union is. rather, .a decreasing- tifnrtinn
of the time or of the number of intervening members. It is
therefore smaller in proportion as theinterval which separates
the individual members is greater. Let a, b, c, d be a series
which has been presented in a single conscious act, then the con-
nection of a with b is stronger than that of a with the later c;
and the latter again is stronger than that with d. If a is in any
way reproduced, it brings with it b and c and d, but b, which is
bound to it more closely, must arise more easily and quickly than
c, which is closely bound to b, etc. The series must therefore
reappear in consciousness in its original form although all the
members of it are connected with each other.
Such a view as this has been logically worked out by Herbart.
He sees the basis of the connection of immediately successive
ideas not directly in the unity of the conscious act, but in some-
thing similar: opposed ideas which are forced together in a
Retention as a Function of Order of Succession 93
unitary mind can be connected only by partial mutual inhibition
followed by fusion of what remains. Yet this, for our purpose,
is not essential. He proceeds as follows:
" Let a series, a,b,c,d . . . be given in perception, then
a, from the very first moment of the perception and during its
continuance, is subjected to inhibition by other ideas present in
consciousness. While a, already partially withdrawn from full
consciousness, is more and more inhibited, b comes up. The
latter, at first uninhibited, fuses with the retiring a. c follows
and, itself uninhibited, is united with the fast dimming b and the
still more obscured a. In a similar fashion d follows and unites
itself in varying degrees with a, b, and c. Thus there originates
for each of these ideas a law according to which, after the
whole series has been forced out of consciousness for some time,
in its own way on its renewed appearance each idea struggles
to call up every other idea of the same series. Suppose that a
arises first, it is more closely connected with b, less with c, still
less with d, etc. But, taken in the reverse order b, c, and d,
all in an uninhibited condition, are fused with what remains of a.
Consequently a seeks to bring them completely back to the form
of an uninhibited idea; but its effect is quickest and strongest
upon b, slower on c and still slower on d, etc. (whereby closer
'.inspection shows that b sinks again while c is still rising, and
that in the same way c sinks while d rises, etc.). In short, the
series runs off as it was originally given. Tf we suppose, on the
contrary, that c was the one initially reproduced, then its effect
on d and the succeeding members is similar to that revealed by
a — i.e., the series c, d, . runs off gradually in con-
formity with its order, b and a, however, experience an alto-
gether different influence. With their separate conscious resi-
dues, the uninhibited c had fused; its effect upon a and b was
therefore wjthout loss of power and without delay, but this
effect was limited to bringing back the conscious residues of a
and b bound up with it, only a part of b and a still smaller part
of a being recalled to consciousness. This, then, is what happens
if the process of recall begins anywhere at the middle of a known
series. That which preceded the point of recall rises at once
in graded degrees of clearness. That which followed, on the
contrary, runs off in the order of the original series^ The series,
94 Memory
however, never runs backwards, an anagram is never formed out
of a well understood word without voluntary effort."1
According to this conception, therefore, the associative threads,
which hold together a remembered series, are spun not merely
between each member and its immediate successor, but beyond
intervening members to every member which stands to it in any
close temporal relation. The strength of the threads varies with
the distance of the members, but even the weaker of them must
be considered as relatively of considerable significance.
The acceptance or rejection of this conception is clearly of
great importance for our view of the inner connection of mental
events, of the richness and complexity of their groupings and
organisation. But it is clearly quite idle to contend about the
matter if observation is limited to conscious mental life, to the
registration of that which whirls around by chance on the surface
of the sea of life.
For, according to the hypothesis, the threads which connect
one member to its immediate successor although not the only
one spun, are, however, stronger than the others. Consequently,
they are, in general, as far as appearances in consciousness are
concerned, the important ones, and so the only ones to be
observed.
On the other hand, the methods which lie at the basis of the
researches already described permit the discovery of connections
of even less strength. This is done by artificially strengthening
these connections until they reach a definite and uniform level of
reproducibility. I have, therefore, carried on according to this
method a rather large number of researches to test experimentally
1 Herbart, Lehrb. z. Psychol., Sect. 29. A similar " pleasing " view,
as he calls it, was developed by Lotze, Metaphysik (1879) p. 527, with
the modification that he attempts to eliminate the notion of varying
strength of the ideas, which view he rejects. In accordance with the
view mentioned first above, he sees the real reason for a faithful repro-
duction of a series of ideas in the fact that association is made only
from one link to the following link. Accordingly, he teaches, in his
Lectures on Psychology (p. 22), "Any two ideas, regardless of con-
tent, are associated when they are produced either simultaneously or
in immediate succession — i.e., without an intervening link. And upon
this can be based without further artifice the special ease with which
we reproduce a series of ideas in their proper order but not out of
that order. By " further artifice " he seems to mean Herbart's attempt
at an arrangement.
Retention as a Function of Order of Succession 95
in the field of the syllable-series the question at issue, and to
trace an eventual dependence of the strength of the association
upon the sequence of the members of the series appearing in suc-
cession in consciousness.
Section 36. Methods of Investigation of Actual Behavior
Researches were again carried out with six series of i6-syllables
each. For greater clearness the series are designated with Roman
numbers and the separate syjlajjles with Arabic. A syllable group
of the following form constituted, then, each time the material
for research:
1(1) 1(2) 1(3)
If I learn such a group, each series by itself, so that it can be
repeated without error, and 24 hours later repeat it in the same
sequence and to the same point of mastery, then the latter repe-
tition is possible in about two thirds of the time necessary for
the first.1 The resulting saving in work of one third clearly
measures the strength of the association formed during the first
learning between one member and its immediate successor.
Let us suppose now that the series are not repeated in pre-
cisely the same order in which they were learned. The syllables
learned in the order I(i) 1(2) 1(3) . . . 1(15) I(i6)
may for example be repeated in the order I(i) 1(3) 1(5)
1 1 have omitted to present a few tests with series of 16 syllables
each from which this number was obtained, because the results of the
sixth chapter sufficiently cover this point. There (p. 55), we saw
that six series of 16 syllables each, each series being repeated 32 times,
could be memorised after 24 hours in an average of 863 seconds. 32
repetitions are, on an average, just necessary to bring about the first
possible reproduction of series of 16 syllables each. Considering the
close proportion which exists between the number of repetitions on a
given day and the saving of work on the next, it cannot much matter
whether the series were repeated, each 32 times, or were memorised
each to the first possible reproduction. Since the latter requires about
1,270 seconds, the work of repetition on the following day amounts,
as stated above, to about two thirds of this time. The relative saving
when i6-syllable series are relearned after 24 hours, is, therefore, scarcely
different from that found for series of 12 and 13 syllables (Chapters
VII and VIII), while it gradually increases for still greater length of
series.
\
96 Memory
. . . I(i5).I(2) 1(4) ,1(6) . . . I (16), and the re-
maining series with a similar transformation. There will first
be, accordingly, a set composed of all the syllables originally in
the odd places and then a set of those originally in the even
places, the second set immediately following the first. The new
i6-syllable series, thus resulting, is then learned by heart. What
will happen? Every member of the transformed series was, in
the original series, separated from its present immediate neighbor
by an intervening member with the exception of the middle term
where there is a break. If these intervening members are actual
obstructions to the associative connection, then the transformed
series are as good as entirely unknown. In spite of the former
learning of the series in the original sequence, no saving in work
should be expected in the repetition of the transformed series.
If on the other hand in the first learning threads of association
are spun not merely from each member to its immediate suc-
cessor but also over intervening members to more distant syllables,
there would exist, already formed, certain predispositions for
the new series. The syllables now in succession have already
been bound together secretly with threads of a certain strength.
In the learning of such a series it will be revealed that noticeably
less work is required than for the learning of an altogether new
series. The work, however, will be greater than in relearning
a given series in unchanged order. In this case, again, the saving!
in work will constitute a measure of the strength of the asso-|
ciations existing between two members separated by a third.
flf from the original^ jirrangement of the syllables new series are
formed by the £>missidn\ of 2, 3, or more intervening members,
analogous considerations result. The derived series will either
be learned without any noticeable saving of work, or a certain
saving of work will result, and this will be proportionally less
as the number of intervening terms increases.
On the basis of these considerations I undertook the following
experiment. I constructed six series of 16 syllables each with the
latter arranged by chance. Out of each group a new one was
then constructed also composed of six series of 16 syllables each.
These new groups were so formed that their adjacent syllables
had been separated in the original series by either i, or 2, or 3,
or 7 intervening syllables.
Retention as a Function of Order of Succession 97
If the separate syllables are designated by the positions which
they held in the original arrangement, the following scheme
results :
1(1) 1(2) 1(3)
via) ................................................................. ;..vi(i6)
By using the same scheme the derived groups appear as follows :
By Skipping 1 Syllable
1(1) 1(3) 1(5) ................ 1(15) 1(2) 1(4) 1(6)... K16)
iid) IKS) IIP) ........... ii(i5) lib) n(4) n(6) ...... ::::::::
VI(3) ...................... 71(15) VI(2) VI(4)
By Skipping 2 Syllables
11$ T?$ I(10) I(13)r&S rl$ T?^ I(8) I(U) I(14) I(3) I(6) KW W2) K15)
1) 11(4) 11(7) ............ 11(16) 11(2) 11(5) ............ 11(14) 11(3) 11(6) ........... . 11(16)
VI(4) ................. VI(16) VI(2) VI(5) ............ VI(14) VI(3) VI(6)
By Skipping 3 Syllables
$\l »!$ I(9) I(13) I(2) I(6) I(10) I(14) I(3) I(7) I^11) KW> K4) K8) 1(12) 1(16)
11(1) 11(5) ............ 11(2) 11(6) ............ 11(3) 11(7) ............ 11(4) 11(8)...... 11(16)
VI(5) ............ VI(2) VI(6) ......... "... VI(3) VI(7) ............ VI(4) VI(8) ......
By Skipping 7 Syllables
1(1) 1(9) 11(1) 11(9) III(l) 111(9) IV(1) IV(9) V(l) V(9) VI(1) VI(9) 1(2) 1(10) 11(2) 11(10)
111(2)111(10) IV(2)IV(10) V(2) V(10) VI(2)VI(10) 1(3) 1(11) 11(3) 11(11) 111(3)111(11) 1V(3)IV(11)
As a glance at this scheme will show, not all the neighboring
syllables of the derived series were originally separated by the
number of syllables designated. In some places in order to again
obtain series of 16 syllables, greater jumps were made; but in no
case was the interval less. Such places are, for example, in the
series in which two syllables are skipped, the transitions from
I(i||)to 1(2) and from 1(14) to I(s). In the series in which
7 intermediates were jumped, there are seven places where there
was no previous connection between successive syllables since
the syllables in question came from different series and the dif-
ferent series, as has been often mentioned, were learned inde-
pendently. The following is given in illustration: 1(9) II (i),
11(9) III(i), etc- Tne number of these breaks varies with
the different kinds of derivation, but in each case is the same
as the number of skipped syllables. On account of this difference,
98 Memory
the derived series suffer from an inequality inherent in the nature
of the experiment.
In the course of the experiment the skipping of more than 7
syllables was shown to be desirable, but I refrained from carry-
ing that out. The investigations with the six i6-syllable series
were carried quite far; and if series had been constructed using
greater intervals, the breaks above mentioned would have had
too much dominance. The derived series then contained ever
fewer syllable-sequences for which an association was possible
on the basis of the learning of the original arrangement; they
were ever thus more incomparable.
The investigations were carried on as follows : — Each time the
six series were learned in the original order and then 24 hours
later in the derived and the times required were compared. On
account of the limitation of the series to those described above
the results are, under certain circumstances, open to a serious
objection. Let it be supposed that the result is that the derived
series are actually learned with a certain saving of time, then
this saving is not necessarily due to the supposed cause, an asso-
ciation between syllables not immediately adjacent. The argu-
ment might, rather, run as follows. The syllables which are
first learned in one order and after 24 hours in another are in
both cases the_ samesyllables. By means of the first learning
they are impressed nof merely in their definite order but also
purely as_ individual syllables ; with repetition they become to
some extent familiar, at least more familiar than other syllables,
which had not been learned just before. Moreover the new
series have in part the same initial and final members as the
old. Therefore, if they are learned in somewhat less time than
tTie first series .required, it is not to be wondered at. The basis
of this does not necessarily lie in the artificial and systematic
change of the arrangement, but it possibly rests merely on the
| identity of the syllables. If these were repeated on the second
day in a new arrangement made entirely by chance they would
probably show equally a saving in work.
In consideration of this objection and for the control of the
remaining results I have introduced a further, the fifth, kind of
derived series. The initial and final syllables of the original
series were left in their places. The remaining 84 syllables, inter-
mediates, were shaken up together and then, after chance
Retention as a Function ,>/ Order of Succession
99
drawing, were employed in the construction of new series between
the original initial and final series. As a result of the learning
of tJ- original and derived series there must in this case also /
be -vealed how much of the saving in work is to be ascribed
merely to the identity of thejyjlablejmasses and to the identity/
oLthejnitiaJ_Jaj^d_fi
Section 37. Results. Associations of Indirect Sequence
For each group of original and derived series n double tests
were instituted, 55 therefore in all. These were distributed
irregularly over about 9 months. The results were as follows :
1) With derivation of the series by skipping one intermediate syllable.
The original series were
learned in x seconds
The corresponding de-
rived series, in y seconds
The latter, therefore,
with a saving of z seconds
•s^
y=
z=
1187
1095
92
1220
1142
78
1139
1107
32
1428
1123
305
1279
1155
124
1245
1086
159
1390
1013
377
1254
1191
63
1335
1128
207
1266
1152
114
1259
1141
118
m 1273
1121
152
2) With derivation of the series by skipping two intermediate syllables.
X
y=
z —
1400
1185
215
1213
1252
—39
1323
1245
78
1366
1103
263
1216
1066
150
1062
1003
59
1163
1161
2
1251
1204
47
1182
1086
96
1300
1076
224
1276
1339
—63
m 1250
1156
94
ioo Memory
3) With derivation of the series by skipping three intermediate syllables.
The original series were
learned in x seconds
The corresponding de-
rived series, in y seconds
The latter, therefore,
with a saving of z seconds
x=
y=
z=
1282
1347
—65
1202
1131
71
1205
1157
48
1303
1271
32
1132
1098
34
1365
1235
130
1210
1145
65
1364
1176
188
1308
1175
133
1298
1209
89
1286
1148
138
m 1269
1190
78
4) With derivation of the series by skipping seven intermediate syllables.
x==
-y— — -
z=
1165
1086
79
1265
1295
—30
1197
1091
106
1295
1254
41
1233
1207
26
1335
1288
47
1321
1278
43
1344
1275
69
1322
1328
—6
1224
1212
12
1294
1217
77
m 1272
1230
42
5) With derivation of the series by retaining the beginning and end
syllables and arranging the remainder by chance.
1305
1302
3
1181
1259
—78
1207
1237
—30
1401
1277
124
1278
1271
7
1302
1301
1
1248
1379
—131
1237
1240
—3
1355
1236
119
1214
1142
72
1147
1101
46
m 1261
1250
12
Retention as a Function of Order of Succession 101
To summarize the results : The new series formed by skipping
i, 2, 3 and 7 intermediate members were learned with an average
saving of 152, 94, 78 and 42 seconds. In the case of the con-
struction of a new series through a mere permutation of the
syllables, there was an average saving of 12 seconds.
In order to determine the significance of these figures, it is
necessary to compare them with the saving in work in my case
in the relearning of an unchanged series after 24 hours. This
amounted to about one third of the time necessary for the first
learning in the case of i6-syllable series, therefore about 42O/
seconds.
This number measures the strength of the connection existing
between each member and its immediate sequent, therefore the
maximal effect of association under the conditions established.
If this is taken as unity, then the strength of the connection of
each member with the second following is a generous third and
with the third following is a scant fourth.
The nature of the results obtained confirm — for myself and
the cases investigated — the second conception given above and
explained by means of a quotation from Herbart. With repeti-
tion of the syllable series not only are the individual terms asso-
ciated with their immediate sequents but connections are also
established betwen each term and several of those which follow
it beyond intervening members. To state it briefly, there seems
to be an association not merely in direct but also in indirect suc-
cession. The strength of these connections decreases with the
number of the intervening numbers ; with a small number it was,
as will be admitted, of surprising and unanticipated magnitude.
No evidence has been secured, however, establishing the facili-
tation of the process of relearning a series by means of the identity
of the syllables and the identity of the initial and final terms.
Section 38. Experiments with Exclusion of Knowledge
I have hitherto not stated the probable errors of the results,
in order to discuss their reliability more fully at this time.
When I started upon the experiment I had no decided opinion
in favor of the final results. I did not find facilitation of the
learning of the derived series essentially more plausible than the
opposite. As the numbers more and more bespoke the existence
io2 Memory
of such facilitation, it dawned upon me that this was the correct
and natural thing. After what has been said above (p. 2jfi)
one might think that in the case of the remaining experiments,
this idea has possibly favored a more attentive and therefore
quicker learning of the derived series, and so has, at least,
decidedly strengthened the resulting saving in work, even if it
has not caused it altogether.
For the three largest of the numbers found, — consequently, for
the facilitation of the work which took place in the case of the
omission of I, 2, and 3 intervening syllables — this objection is of
slight significance. For these are proportionately so large that
it would be attributing too much to an involuntary heightening
of a state of attention, voluntarily coricentratecf without this to
fhe utmost, if an actual influence is ascribed to it here. More-
over, the gradation of the numbers, decisively issuing as they do
from the distribution of the individual values and running parallel
with the number of skipped intermediate terms, is inconceivable
on any such hypothesis as this. For the supposed greater con-
centration of the attention could clearly work only in general.
How could it possibly bring about so regular a gradation of
numbers in the case of tests which were separated from each
other by weeks and months?
The objection presented above could render doubtful only the
fourth result, the proportionally slight saving in the learning of
.series formed frorrT"^fEeTyerTes"by ^kipping seven intermediate
terms. ^
Clearly in this case the exact determination of the difference
is of especial interest because of the significant size of the interval
over which an association took place.
In the case of the present investigations there exists the pos-
sibility of so arranging them that knowledge concerning the out-
come of the gradually accumulating results is excluded and so
that consequently the disturbing influence of secret views and
desires disappears. I have accordingly instituted a further group
of 30 double tests in the following way as a control of the above
results, and especially of the least certain of them.
On the front side of a page were written six i6-syllable series
selected by chance and on the reverse side of the same sheet six
series formed from them by one of the methods of derivation
described above (p. 97). For each of the five transforma-
Retention as a Function of Order of Secession 103
tions 6 sheets were prepared. The fronts and backs of these
could be easily distinguished but not the sheets themselves. The
thirty sheets were shuffled together and then laid aside until
any memory as to the occurrence of the separate syllables in
definite transformations could be considered as effaced. Then
the front side, and 24 hours later, the reverse side of a given
sheet were learned by heart. The times necessary for learning the
separate series were noted, but they were not assembled and
further elaborated until all 30 sheets had been completed. Fol-
lowing are the numbers.
1) With derivation of series transformed by skipping one intermediate
syllable.
The original series were
learned in x seconds
The corresponding de-
rived series, in y seconds
The latter, therefore,
with a saving of z seconds
1137
1292
1202
1272
1436
1340
y=
1081
1045
1237
1202
1299
1157
z=
56
247
—35
70
137
183
m 1280
1170
110
2) With derivation of the series by skipping two intermediate syllables.
x=
y=
z=
1415
1232
183
1201
1290
—89
1291
1156
135
1358
1153
205
1232
1254
—22
1168
1107
61
m 1278
1199
79
3) With derivation of the series by skipping three intermediate syllables
x=
•\7
z=
1205
1166
39
1339
1068
271
1179
1293
—114
1238
1196
42
1257
1231
26
1240
1122
118
m 1243
1179
64
Memory
4) With derivation of the series by skipping seven intermediate syllables.
The original series were
learned in x seconds
The corresponding de-
rived series, in y seconds
The latter, therefore,
with a saving of z seconds
1191
1191
1237
1350
1308
1289
•y— —
1120
1185
1295
1306
1260
1158
z==
71
6
—58
44
48
131
m 1261
1221
40
5) With derivation of the series by retaining the first and last syllables
in position and changing the rest by chance.
x=
•y
z=
1305
1180
125
1206
1205
1
1310
1426
—116
1163
1089
74
1272
1388
—116
1309
1305
4
m 1261
1266
—5
By derivation of the transformed series by skipping I, 2, 3, 7
intermediate syllables, the derived series were therefore learned
with an average saving of 1 10, 79, 64, 40 seconds. On the con-
trary with derivation of the series by permutation of the syllables
the learning required an average increase in expenditure of 5
seconds.
Taken as a whole, these last results exactly confirm, as can
be seen, the result that was obtained at the beginning. The num-
ber of these experiments was proportionally small and, during
the course of each experiment, there was complete exclusion of
knowledge as to results. In spite of these facts and although
the numbers, considered individually, seem to be distributed
without regard to law, their grouping, when taken as a whole, is
seen to be in conformity to a simple law. TJie_fewer_are__the
intervening-members -jadiich separate two^syjiables of a series
icfi has been learnedjby riea.rt,Jhe lessjsjhe resistance offered
oy these separated syllables to their being tearneiHn a new order.
Retention as a Function of Order of Secession 105
And, in the same way, the fewer are these intervening terms, the
stronger are the bonds which, as a result of the learning of the
original series, connect the two syllables across the intervening
members.
In addition to agreeing in their general course, the numbers for
both groups of experiments also agree in the following respect
The difference between the first and second numbers has the/
greatest value, and that between the second and third has the least
j^aluer~On~fEe other hand, it is surprising that, with respect to
their absolute size, the numbers of the second group are through- i
out smaller than those of the first. Two causes may be broughT
forwarder? explanation of this behavior, which, considering the
conformity of the numbers, can scarcely be accidental. It may
be that here is actually revealed that influence of expectation
which has already been mentioned. On the basis of this
hypothesis, the explanation of the fact that the numbers of
the first group come out somewhat too large is that, in the
course of the experiment, the existence of a saving in work
in the case of the derived series was anticipated, and for this
reason the learning of the series took place involuntarily with a
somewhat greater concentration of attention. On the other
hand, it may be that, in consequence of the excluded knowledge,
there has been at work in the case of the numbers of the second
group a disturbing element which has made them smaller. Here,
to be sure, during the learning of the derived series a very lively
curiosity developed concerning the category of transformation
to which the series which had just been learned belonged. That
this must have had a distracting, and therefore retarding, in-
fluence is probable not only in itself but also through the result
obtained from the series derived by permutation of syllables.
It was to be expected that the identity of the syllables, as well
as of the initial and end terms, would make itself felt in this
case by a saving of work, however small that saving might be.
The latter effect appears, it is true, in the experiments of the
first group. With those of the second group, however, there is
noticeable, instead of this saving of work, a slight additional
expenditure of time. This, if it is not merely accidental, can
scarcely be explained otherwise than through the distracting
curiosity mentioned.
It is possible that both influences were at work simultaneously
io6
Memory
so that the first experiments gave results which were somewhat
too high; and the second, results that were somewhat too low.
It is allowable, under this hypothesis, to put the two sets of
figures together so that the contrasting errors may compensate
each other. In this way there was finally obtained out of the
85 double tests the following table.
Number of
intermediate
syllables skipped
in the forma-
tion of the
Time for
learning
the
original
series
Time for
learning
the
derived
series
Saving of
work in
learning
the derived
series
Probable
error of
saving
of work*
Saving of
work in %
of original
learning
time
derived series
(The numbers of the four middle columns denote seconds)
0
(1266)
(844)
(422)
(33.3)
1
1275
1138
137
± 16
10.8
2
1260
1171
89
± 18
7.0
3
1260
1186
73
± 13
5.8
7
1268
1227
42
± 7
3.3
permutation
of syllables
1261
1255
6
± 13
0.5
* The probable errors are calculated from the separate values for savings
of work, while the latter, which were actually obtained by subtraction,
are considered as the results of direct observation. (See p. 67, note.)
Section 39. Discussion of Results
In the foregoing table an especial interest, it seems to me,
is connected with the last, and also with the next to the last,
row of numbers. When there was complete identity of all the
syllables and the initial and end terms were left in their places,
the average saving of time for 17 tests dealing with the learning
of the derived series was so slight that it was hardly to be
determined. It fell within half of its probable error. The
syllables were, therefore, in themselves, outside of their con-
nection, so familiar to me that they did not become noticeably
more familiar after being repeated 32 times. On the contrary
when a related series was repeated the same number of times,
each syllable became so firmly bound to the syllable which fol-
lowed 8 places beyond that 24 hours later the influence of this
connection could be determined in no doubtful fashion. It
attains a value 6 times the probable error. Its existence, there-
fore, must be considered to be fully proved although naturally
we cannot be so sure that its size is exactly what it was found
Retention as a Function of Order of Succession 107
to be in the experiments. Although its absolute value is small,
yet its influence amounts to one tenth of that of the connection
which binds every member to its immediate successor. It is so
significant, and at the same time the decrease in the after-effect
of connections which were formed over 2, 3, 7 intervening mem-
bers is so gradual a one, that the assertion can be made, on
these grounds alone, that even the terms which stand still
further from one another may have been bound to each other
subconsciously by threads of noticeable strength at the time of
the learning of the series.
I will summarise the results so far given in a theoretical
generalisation. As a result of the repetition of the syllable-
series certain connections are established between each member
and all those that follow it. These connections are revealed by
the fact that the syllable-pairs so bound together are recalled
to mind more easily and with the overcoming of less friction
than similar pairs which have not been previously united The \
strength of the connection, and therefore the amount of workx
which is eventually saved, is a decreasing function of the timej
or of the mimber of the intervening members which separated ;
the syllables in question from one another in the original series. y
It is a maximum for immediately successive members. The/
precise character of the function is unknown except that it'
decreases at first quickly and then gradually very slowly witty
the increasing distance of the terms.
If the abstract but familiar conceptions of ' power,' ' disposi-
tion,' be substituted for the concrete ideas of saving in work
and easier reproduction, the matter can be stated as follows.
As a result of the learning of a series each member has a
tendency, a_1g,tent disposition,, to draw after itself, at its own
return to consciousness, all the members of the series which
followed it. These tendencies are of varying strength. They
are the strongest for the members which immediately follow.
These tendencies are accordingly in general most easily demon-
strable in consciousness. The series will return in its original
form without the intervention of other influences while the
forces directed to the resuscitation of the remaining members
can be explicitly demonstrated only by the introduction of other
conditions.
io8 Memory
It is naturally not conceivable that by a mere caprice of
nature the validity of the principles discovered should be limited
exclusively to the character of the material in which they were
obtained — i.e., to series of nonsense syllables. They may be
assumed to hold in an analogous way for every kind of idea-
series and for the parts of any such series. It goes without
saying, wherever relations exist between the separate ideas,
other than those of temporal sequence and separation by inter-
mediate members, these forces will control the associative flow,
not exclusively, but with reference to all the modifications and
complications introduced by relations of various affinities, con-
nection, meaning, and the like.
At any rate, it will not be denied that the doctrine of Asso-
ciation would gain through a general validity of these results a
genuine rounding out and, so to say, a greater reasonableness.
The customary formulation, " ideas become associated if they
are experienced simultaneously or in immediate succession," has
something irrational about it. If the immediacy of succession
is taken precisely, the principle contradicts the most common
experiences. If it is not taken exactly, then it is hard to state
' what kind of sequence is properly meant. At the same time
it is not clear why a sequence not quite direct should have an
advantage which suddenly disappears in the case of a sequence
still more indirect. As we now know, the directness or indirect-
ness of the sequence is without effect upon the general nature of
what happens between ideas which succeed each other. \ In both
cases connections are formed which on account of. their com-
plete similarity can be designated only by the common term,
Association. But these are of different strength. As the sue- /
cession of united ideas approaches ideal immediacy the connect-
ing threads grow stronger, and in proportion as it departs from
this ideal, these threads grow weaker. The associations between
more distant terms, although actually present and demonstrable
under proper conditions have, nevertheless, on account of their
I slight strength, practically no significance. The associations
/ between adjacent terms are, on the contrary, of relatively great
/ importance, and will make their influence abundantly felt. Of.
course, if the series were left entirely to themselves and if they
were always produced in precisely the same order, for each
term there would appear only one association, the relatively
Retention as a Function of Order of Succession 109
strongest — namely, that with the immediately succeeding tenn.
But series of ideas are never left to themselves. The rich and
quickly changing order of events brings them into the most
manifold relations. They return with their members in the most
varied combinations. And then, under certain circumstances,
the stronger of these less strong associations between more dis-
tant terms must find opportunity to authenticate their existence
and to enter into the inner course of events in an effective way.
It is easy to see how they must favor a more rapid growth, a
richer differentiation, and a many-sided ramification of the ideas
which characterise the controlled mental life. Of course they
also favor a greater manifoldness, and so apparently a greater
arbitrariness and irregularity, in mental events.
Before I proceed further, I wish to add a few words con-
.cerning the above mentioned (p. 91) derivation of the asso-
ciation of successive ideas from the unitary consciousness of a
unitary soul. There is a certain danger in bringing together a
present result with one found previously. I mentioned above
(p. 47) that the number of syllables which I can repeat without
error after a single reading is about seven. One can, with a
certain justification, look upon this number as a measure of the
ideas of this sort which I can grasp in a single unitary conscious
act. As we just now saw, associations are formed of noticeable
strength over more than seven intervening members, therefore
between the beginning and end of a nine-syllable series. And
on account of the size of the numbers obtained and the nature
of their gradation, it seems probable that, even with a larger
number of syllables, connections would be formed between their
extremes. If, however, associations are built between members
too far separated to be held together in a single conscious act,
it is no longer possible to explain the presence of those asso-
ciations on the basis of the simultaneous presence of the united
ideas in consciousness.
However, I recognise that those for whom such a derivation
is a cherished matter are not necessarily forced by the above
discussion to abandon their conception. Such are those who
consider the unitary acts of a unitary soul as something more
original, intelligible, transparent or better worthy of belief than
the simple facts of association described above, so that the
reduction of the latter to the former would be a noteworthy
no Memory
achievement. One needs but to say that, in the case of an
unfamiliar sequence of syllables, only about seven can be
grasped in one act, but that with frequent repetition and gradu-
ally increasing familiarity with the series this capacity of con-
sciousness may be increased. So, for example, a series of 16
syllables, which have been thoroughly memorised, may be present
in a single conscious act. Accordingly this " explanation " is
freely available. Those for whom it was of value in the case
of association by simultaneity or immediate succession can
employ it fully as well for our case of indirect sequence. And
because of the modest requirements which in psychology are so
often imposed upon explanations, this view will doubtless for
a long time serve to make dim the vision and so prevent the
frank recognition of this as one of the most wonderful of all
riddles, and it will also act as a hindrance in the search for its
true understanding.
Section 40. Reverse Associations
Of the many problems which spring out of the results pre-
sented,! have been able for the time being to investigate only
a few and these by means of only a small number of experiments.
As a result of the frequent repetition of a series — a, b, c, d
. — certain connections — ab, ac, ad, bd, etc. — are
formed. The idea a, whenever and however it returns to con-
sciousness, has certain tendencies of different strength to bring
also with it to consciousness the ideas b, c, d. Are now these
connections and tendencies reciprocal? That is, if at any time
r and not a is the idea by some chance revived, does this have,
dn addition to the tendency to bring d and e back with it, a
similar tendency in the reverse direction towards b and af In
other words : — As a result of the previous learning of a, b, c^ d,
the sequences a, b, c; a, c, e, are more easily learned than any
grouping of equal length of syllables previously unknown such
as p, q, r. . . . Is the same thing true of the sequences
c b a, and e c a? As a result of manifold repetition of a series
are associations also formed in the reverse order?
The views of the psychologists seem to be divergent upon this
point. One side call attention to the undoubted fact that in
spite of complete mastery of, say, the Greek alphabet a person
Retention as a Function of Order of Succession 1 1 1
is not at all in a position to repeat it readily backwards if he
has not specially studied and practiced it in this form.
The other side make extensive use of reverse associations, as
of something quite intelligible, in their explanation of the origin
of voluntary and purposive movements. According to them the
movements of the child are at first involuntary and accidental.
With certain combinations of these, intensely pleasurable feel-
ings result. In the case of movements as of feelings, memory
tracesTemain which, by repetition of the occurrences, are always
more closely associated with each other. If this connection has
attained a certain strength, the mere idea of the agreeable feeling {
leads backwards to the idea of the movement which aroused it ; I
then comes the actual movement and with it also the actual
sensed feeling.
The conception of Herbart, which we learned to know above
(p. 94), holds the middle course between these two views. The
idea c, which appears in the course of a series, fuses with the
ideas b and a, which have preceded it and which are yet present
although becoming dim. If c is later on reproduced, it brings
b and a with it but dimmed, not fully uninhibited or clearly
conscious. With the sudden arousal of a member out of the
midst of a series we survey that which preceded " at once in
graded clearness " ; but never does it happen that the series runs
off in reverse order. To the member which springs up in con-
sciousness there succeed in due order and in complete conscious- 1
ness those terms which followed it in the original series.
For the purpose of testing the actual relations I carried out
an experiment entirely similar to the previously described in-
vestigations. Out of groups each composed of six i6-syllable
series arranged by chance^ new groups were derived either
through mere reversal of the sequence or by that plus the
skipping of an intermediate syllable. Then the two sets of
groups were learned by heart, the derived form 24 hours later
than the original.
If the scheme for the original form is written as follows :
I(i) 1(2) 1(3) I(i5) I(i6), then the corresponding
derived series is thus designated:
In the case of mere reversal of the syllable sequence:
1(2) 1(0,
112
Memory
In the case of reversal plus skipping of an intermediate syllable,
I(i6) I(i4) I(i2). ...1(4) 1(2) I(i5) I(i3). -..1(3) 1(0.
For the first kind of derivation I have carried out ten experi-
ments ; for the second, only four.
The results are as follows :
1) With derivation of the transformed series by mere reversal of the
syllable sequence.
The original series were
learned in x seconds
The corresponding de-
rived series, in y seconds
The latter, therefore,
with a saving of z seconds
•y — - -
y=
z=
1172
1023
149
13r7
1170
147
1215
977
236
1202
1194
8
1257
1031 -
226
1210
1087
123
1285
1051
234
1260
1150
110
1245
1070
175
132.9
1189
140
m 1249
1094
155
P.E.m=15
In relation to the time of learning the original series the saving
amounts to 12.4 per cent.
2) With derivation of the transformed series by reversal and at the same
time by skipping one intermediate syllable.
x==
y=
z=
1337
1291
46
1255
1164
91
1158
1143
15
1313
1224
89
m 1266
1206
60
P.E.m=12
In relation to the time of learning the original series the saving
amounted to 5 per cent.
As a result of the learning of a series certain connectjqns of
the members are therefore actually formed in a reverse as well
as in a forward direction. These connections are revealed in
this way, that series which are formed out of members thus
Retention as a Function of Order of Succession 113
connected are more easily learned than similar series, whose
individual members are just as familiar but which have not
been previously connected. The strength of the predispositions |
thus created was again a decreasing function of the distance of I
the members from each other in the original series, it was, '
however, considerably less for the reverse connections than for
the forward ones, the "distances being equal. With an approxi-
mately equal number of repetitions of the series the member
immediately preceding a given member was not much more
closely associated with it than the second one following it; the
second preceding — so far as may be determined on the basis
of these few researches — scarcely as firmly as the third following. '
If one could assume a more general validity for this relation
found here first in connection with syllable series, the mutually
opposed experiences just mentioned would, I believe, become
thoroughly intelligible. Where a series consists of only two
members — as in the case of the connection between a simple
idea of movement and that of an agreeable feeling — then, by
means of frequent repetition the end term will acquire so strong
a tendency to call up after itself the initial term that the latte^
will actually appear. For the bringing up of the term first pre-
ceding it is the only thing for which, as a result of the many
repetitions, the second term has acquired a predisposition. But,
no matter how many repetitions there may be in the case of a
long series, it will never happen on the arousal of a middle term
that the series will reappear in a reverse order. For, however
easily the immediately preceding term may connect itself with
the one for the moment aroused, the immediately succeeding
term will appear more easily by far, and so will win the victory,
provided other influences do not intervene.
No matter how thoroughly a person may have learned the
Greek alphabet, he will never be in a condition to repeat it
backwards without further training. But if he chances to set
out purposely to learn it backwards, he will probably accomplish
this in noticeably shorter time than was the case in the previous
learning in the customary order. The objection is not in point
that a poem or speech which has been committed to heart is
not necessarily learned more quickly backwards than it was
originally forwards. For with the learning in reverse direction
the numerous threads of inner connection on which rapid learn-
ii4 Memory
ing of meaningful material in general depends will be brought
to nothing.
Section 41. The Dependence of Associations of Indirect
Sequence upon the Number of Repetitions
The connection set up as a result of many repetitions between
the immediately succeeding members of an idea- or syllable-
series is a function of the number of repetitions. As a result
of the investigations of Chapter VI, which were purposely di-
rected to the discovery of this relation, an approximate pro-
portionality, within tolerably wide limits, has been made out
between the number of repetitions and the strength of the con-
nections established by them. The latter was measured, pre-
cisely as in the investigations of the present chapter, by the
amount of work saved in relearning the connected series after
24 hours.
If now, as a result of repetitions, connections are also set
up between members of a series which are not immediately suc-
cessive, the strength of the latter is naturally also in some way
dependent upon the number of repetitions. The question arises
in what form the different dependence occurs in this case. Does
a proportionality exist here also? If the number of repetitions
is made greater, will the threads of separate strength, which
bind together all the members of a series learned by heart, in-
crease in strength in the same proportion ? Or is the nature and
rate of their increase in strength a different one as is the case
with the strength of the threads themselves? On the basis of
our present knowledge neither the one nor the other of these
possibilities can be declared self-evident.
To facilitate an insight into the actual conditions I have insti-
tuted a few preliminary experiments in the following way. Six
series of 16 syllables each were impressed upon the memory
by a 1 6- or 64- fold attentive repetition. After 24 hours an
equal number of derived series of the same length, which had
been obtained from those already learned by skipping one inter-
mediate syllable, were learned by heart to the first repetition.
In order to make the investigations useful in other ways, the
series were derived in this case by a method somewhat different
from that described above (p. 97). The latter method differs
Retention as a Function of Order of Succession 1 1 5
from the former in that here the odd-numbered syllables of the
original series were not followed by the even-numbered syllables
of the same series. But all the odd-numbered syllables of two
original series were united to form a. new i6-syllable series.
Then the even-numbered syllables of the same original series
were united to form a second new series. The scheme of the
derived series was therefore not, as above,
1(1) 1(3) 1(5) 1(15) 1(2) 1(4) 1(16),
11(1) 11(3) 11(5) 11(15) 11(2) 11(4) 11(16),
but rather
1(1) 1(3) 1(5) 1(15) 11(1) 11(3)
1(2) 1(4) 1(6) 1(16) 11(2) 11(4) II(16)
The effect of the derivation upon the learning of the derived
series, cannot, as it seems, be essentially affected through this
slight change. Here, as in the above described method of deriva-
tion, the syllables which during the first learning had been separ-
ated from each other by an intervening syllable were learned
24 hours later in immediate succession.
For each number of repetitions used in learning I made 8
double tests, which gave the following results:
Number of repetitions employed for the impression of each of
the original series :
16 64
Number of seconds required for learning the six derived series
after 24 hours (including the recital) :
1178 1157
1216 982
1216 1198
950 1148
1358 995
1019 1017
1191 1183
1230 1196
Average 1170 1109
Probable error 30 22
On account of the small number of experiments the result-
ing averages are, unfortunately, not very exact; but the general
character of the results would remain the same even if we
considered the value false within the whole range of the prob-
able error. This character becomes apparent upon comparison
with the values given above (p. 56) for learning by heart six
i6-syllable series which had not previously been learned. This
took place in 1,270 seconds. After the original series had been
n6
Memory
repeated 16 times, the derived series was learned with a saving
of about 100 seconds ; after repetition 64 times, with a like saving
of 161 seconds. Quadrupling the repetitions resulted in increas-
ing the saving only a little more than half as much again. The
increase in strength of the associations reaching over an inter-
mediate member was in nowise proportional to the number of
repetitions, for the cases studied, not even within the limits
for which this was noticeably the case for associations from
one member to its immediate successor. On the contrary the
effect of the repetitions in the case of associations of indirect
sequence decreased considerably sooner and more quickly than
in* the case of those of direct sequence.
There is very close agreement between the pair of values just
found and the number given above (p. 99, i) — the procedure be-
ing, as here, without the exclusion of knowledge — for the learning
of derived series which the day before had been learned in their
original form to the point of first possible reproduction. This
number, it is true, was obtained under somewhat different con-
ditions. In the first place, not always were the same number
\ of ^repetitions employed for learning, but each time as many as
were required for the first possible reproduction — i.e., not exactly,
but on the average, 32. Moreover, the nature of the derivation
of the series was somewhat different, as was stated above. But
these differences have little weight in the case of numbers which
otherwise could have little claim to exactness. I adduce there-
fore this value for comparison, and in addition the numbers
given in Chapter VI for the influence of repetitions -on the re-
learning of the same untransformed series. Here then is the
table.
Time for
Time for
relearning
Saving in
Number
relearning
after 24
Saving in
Saving in
changed
of
the untrans-
hours series
relearning
learning
series in %
Repeti-
formed
transformed
unchanged
the changed
of the saving
tions
series after
by skipping
series
series
for the
24 hours
one syllable
unchanged
0
1270
16
1078
1170
192
100
52%
32
863
1121
407
149
37%
64
454
1109
816
161
20%
(The numbers of the four intermediate columns mean seconds.)
Retention as a Function of Order of Succession 117
I call attention again to the fact that the numbers given above
are in part rather inexact and that they were gained under very
limited conditions. However, it is allowable to sketch sum-
marily and with hypothetical elaboration the view which these
results make appear to be the most probable explanation of an
important group of inner processes and which fills pleasingly and
completely a hitherto empty place in our knowledge.
With the imprinting and internal fixation of an idea-series '•
through its manifold repetition, inner connectionsT associa- /
tions, are woven between all the separate members of the
series. The nature of these is such that series made out of
members thus associated are picked up and reproduced more
easily, with less ^resistance to be overcome, than similar series
made up of members not previously associated. Their nature
can also be stated in this way, that each member of the series
has the definite tendency on its own return to consciousness to
bring back others with it. These connections, or tendencies, are
of different strength from several different points of view. For
the more distant members of the original series they are weaker
than for the nearer ; for specific distances backwards they are j
weaker than for the same distances forward. The strength of
all the connections increases as the number of repetitions in-
creases. But the originally stronger threads between the nearer
members are strengthened considerably more quickly than the
weaker ones which connect the more distant terms. The more,
therefore, the number of repetitions increases, the stronger, both
absolutely and relatively, become the connections between imme-
diately successive terms. To the same degree the more exclusive
and dominant becomes the tendency of each term at its own
returfTmto consciousness to draw after itself that term which
had always immediately followed it during the repetitions.
Section 42. Indirect Strengthening of Associations
I conclude with the mention of a noteworthy fact which ap-
peared incidentally in connection with the investigations men-
tioned in the preceding paragraphs. On account of the uncer-
tainty of the numerical results which come into consideration, I
can call attention to it only with great reserve. I cannot, how-
ever, pass it by altogether because it is probable in itself, and
1 1 8 Memory
because, with further confirmation, it will throw a character-
istic light on inner processes which are actually present but
which remain unconscious. It will also reveal the relative/
independence of these processes from conscious accompaniments,
as I have shown above (§ 24).
The derivation of the transformed series in the case of the
last mentioned investigations was accomplished, as has been
stated, in the following way. Out of two i6-syllable series
selected by chance, first all the odd-numbered syllables were
combined to form a new series and then all the even-numbered
to form a second series which followed in immediate succession.
In the case of a group consisting of six series of this sort,
therefore, the derived series II contained nothing but syllables
which in the first process of memorising had followed imme-
diately upon the corresponding members of series I. The derived
series IV bore a similar relation to series III, and series VI to
series V. The following phenomenon appeared, which is the
peculiar relation to which I wish to call attention. Less time
was required for learning by heart series II, IV, VI on the
average than for series I, III, V, although in all the other groups
of series, whether original or derived, the converse was the case.
I adduce some numerical data in evidence of this relation.
From all the experiments with six series of 16 syllables which
were learned to the point of the first recital, ten immediately
successive experiments are chosen by chance for two different
time-periods. The times for committing to memory series I,
III, V are combined in calculation, as are also those for series
II, IV, VI.
Retention as a Function of Order of Succession 119
1
A
B
J
Sum of series
(I, III, V)
Sum of series
(II, IV, VI)
(B-A)
467
790
323
544
666
122
662
704
42
548
668
120
523
539
16
475
657
182
612
753
141
853
548
—305
637
641
4
499
780
281
m 582
675
93
P.E.m=±37
488
694
206
604
704
100
551
734
183
596
637
41
559
686
127
611
744
133
653
682
129
598
700
102
723
606
—117
643
678
35
m 603
687
84
P.E.m=±20
The sum of series II, IV and VI, found by averaging the ten
experiments, is here in both cases, as can readily be seen, con-
siderably greater than the sum of series I, III, V. The differ-
ences are, to be sure, of very different amounts for the separate
experiments, and in one case they have a pronounced negative
value ; but these fluctuations are represented in the large probable
error of the differences of the averages; and, in spite of the
size of these errors, the positive character of the differences
may be considered as fairly certain.
In all other investigated cases the following result appears:
there are large fluctuations of the differences in the individual
experiments, but a combination of the several experiments shows
a decisive^ predominance for series II, IV, VI although the
surplus is smaller than in the case of the two experiments in
question. Thus in the case of n earlier tests in which series
120 Memory
were learned by heart which had been derived by skipping one
intermediate syllable and which had been learned the day before
in the original form the results were (p. 99, i) :
Sum of series (II, IV, VI) minus Sum of series (I, III, V)
=*33 (P.E.m=*23).
With six later tests of the same sort (p. 103, i) :
Sum of (II, IV, VI) minus Sum of (I, III, V) =42 (P.E. m
==29).
With ten experiments with series which had been repeated
the day before 16 times each (p. 55) :
Sum of (II, IV, VI) minus Sum of (I, III, V) = 17 (P.E.m
= 21), etc.
On account of the largeness of the probable error a single one
of the last given figures would have little significance. By means
of their correspondence as to the nature of the difference they
gain in probability, and the phenomenon becomes quite intelligible
in light of the results of Section 18. There, and with especial
clearness in the case of i6-sy liable series, it was shown that the
learning of the individual series occurred in the form of fairly
regular oscillations. These were of such a sort that a relatively
slowly learned series followed one learned relatively more
quickly and vice versa (p. 43, Fig. 3). Since in the case of
each experiment the first series was learned on the average the
most quickly and the second the most slowly, by the combination
of series I, III, V the average minima are united and of series
II, IV, VI the average maxima. The difference, 5* (II, IV, VI)
minus (I, III, V) is, therefore, in general positive.
Accordingly it must be surprising that in the case of both
the groups of tests mentioned in the preceding paragraphs, this
difference is on the contrary of a negative sign.
Retention as a Function of Order of Succession
121
(1) The results in the case of learning derived series which had been re-
peated 16 times on the day previous in their original form were as follows:
A
Sum of
(I, HI, V)
B
Sum of
(II, IV, VI)
J
(B-A)
656
702
603
450
662
560
588
637
522
514
613
500
696
459
603
593
—134
. —188
10
50
34
—101
15
—44
Av. 607
562
-^5 P.E.m ±21
(2) The results of learning derived series which had been repeated 64
times on the day previous in their original form were as follows:
A
Sum of
(I, HI, V)
B
Sum of
(II, IV, VI)
A
(B-A)
515
567
626
588
543
539
584
592
642
415
572
560
452
478
599
604
127
—152
—54
—28
—91
—61
15
12
Av. 569
540
—29 P.E.m ±20
The fluctuations of the numbers for the separate experiments
are also in this case very great. However, it is evident on the
first glance and without further comparison that a strong dis-
placement of the differences to the negative side has taken place.
This fact is also expressed by the averages. In contrast with
previous results, the series II, IV, VI were learned in somewhat
shorter time than series I, III, V.
That this exception rests on mere chance is possible but not
very probable. The piobable errors, although large, are not
large enough to indicate this.
I would sooner fear that it was a case of disturbance of the
results through the oft-mentioned source of error, anticipation
of the outcome (p. 27 ff. and p. 101). During the progress of the
experiment I believed with increasing certainty that I could fore-
122 Memory
see the smaller expenditure of time for the learning of series II,
IV, VI, and it was only because I thought something of this
sort that I changed the method of derivation of the transformed
series. I cannot, therefore, exclude the possibility that, merely
on the basis of this hidden presupposition and in a manner
altogether unrevealed to consciousness, a greater concentration
of attention was present in learning series II, IV, VI than in
learning series I, III, V. However, this assumption is not to
be taken positively as the correct one. The assumption that the
whole of the difference found is to be traced back to the influ-
ence of this source of error would involve the ascription of a
pretty large function to an involuntary and completely uncon-
scious accommodation of attention due to a secret expectation.
There remains, accordingly, a certain probability for the third
possibility, namely, that the contrasting character of the average
differences has in part at least an objective basis, that the more
rapid learning of the derived series, II, IV, VI, was in part
due to their manner of derivation.
" The proper way in which to think of this causation would
become clear only by the introduction of physiological concep-
tions which must first be constructed or at least remodelled.
If use is made of the language of psychology, then, as in the
case of all unconscious processes, expression can be only figura-
tive and inexact.
As a result of the learning by heart of a series in the original
form the separate syllables, we must say, retain fairly strong
tendencies upon their own return to consciousness to bring after
them the syllables which immediately succeeded them. If, there-
fore, the syllables i, 3, 5, etc., return to consciousness, the
syllables 2, 4, 6, etc., have a tendency also to appear. This
tendency is not strong enough to bring about as a consciously,
perceivable event the actual appearance of 2, 4, 6. The latter
are in evidence only in a certain inner condition of excitability;
something takes place in them which would not have occurred
if i, 3, 5 had not been repeated. They behave like a. forgotten
name which one attempts to recollect. This is not consciously
present; on the contrary, it is being sought. In a certain way,
jowever, it is undeniably present. It is on the way to con-
sciousness, as one might say. For if ideas of all sorts were
called up which stood in connection with the earlier experienced
Retention as a Function of Order of Succession 123
name, a person could usually tell whether they agreed with the
one now sought for but not yet found, or not. As a result of
the frequent repetition of the syllables i, 3, 5 previously con-
nected with the syllables 2, 4, 6, the latter were placed in a
similar slightly pronounced condition of excitation, lying between
conscious appearance on the one side and simple non-appearance
on the other. And this excitation has, as it now appears from
our tests, a result altogether similar to that of actual return
to consciousness. Inner connections are established between suc-
cessively and internally aroused syllables just as between syllables
successively raised to consciousness, except that the former are
naturally of less strength. Secret threads are spun which bind
together the series 2, 4, 6, not yet aroused to consciousness, and
prepare the way for its conscious appearance. Such threads
existed already in greater strength as a result of the learning
of the original series ; the present effect is that of strengthening
somewhat connections already made. And that is nothing else
than what was found above: if two syllable-combinations — I,
3, 5 . . . and 2, 4, 6 . . . — are frequently asso-
ciated in consciousness (the learning of the original series) then
the subsequent learning of the second combination (derived
series II, IV, VI) soon after the learning of the first (derived
series I, III, V) has considerably less resistance to overcome
than the latter. A certain strengthening of associations takes — >v
place, not only directly, through conscious repetition of the asso-
ciated members, but also indirectly through the conscious repe- /
tition of other members with which the first had been frequently^
connected.
This way of viewing the matter is a consequence of the as-
sumption (which became necessary above, p. 109) of the forma-
tion of associative connections over more intervening members
than could be comprehended in one clearly conscious act. These
connections would be very fruitful in the explanation of many
surprising phenomena of memory and recollection, but on ac-
count of the uncertainty of their experiential basis I refrain for
the present from pursuing them further.
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